Calculating Present Value of Annuity with Increasing Payments
Learn how to determine the present value of an annuity with annual payments starting at $3 and increasing by $3 with each subsequent payment until reaching a final payment of $45, all at a 6% annual effective interest rate.
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Presentation Transcript
SOA Exam FM Module 2 Section 6 Arithmetic Annuity Example
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate.
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 ??
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 ( = 3) ??
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 45 = 3 15 3 6 45 ( = 3) ??
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 ?? = 3(? ?)15|
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 ?15| 15?15 ? ?? = 3(? ?)15|= 3
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 ?15| 15?15 ? ?15| 15?15 ? ?? = 3(? ?)15|= 3 = 3 (1 + ?)
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 ?15| 15?15 ? ?15| 15?15 ? ?? = 3(? ?)15|= 3 = 3 (1 + ?) = 3(??)15|(1 + ?)
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 ?15| 15?15 ? ?15| 15?15 ? ?? = 3(? ?)15|= 3 = 3 (1 + ?)
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 ?15| 15?15 ? ?15| 15?15 ? ?? = 3(? ?)15|= 3 = 3 (1 + ?) ? = ?15| 15?15
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 ?15| 15?15 ? ?15| 15?15 ? ?? = 3(? ?)15|= 3 = 3 (1 + ?) ? ?15|+ 15?15= 0 ? = ?15| 15?15
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 ?15| 15?15 ? ?15| 15?15 ? ?? = 3(? ?)15|= 3 = 3 (1 + ?) ? ?15|+ 15?15= 0 ? = ?15| 15?15
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 ?15| 15?15 ? ?15| 15?15 ? ?? = 3(? ?)15|= 3 = 3 (1 + ?) ? ?15|+ 15?15= 0 ? = ?15| 15?15 TVM: ? = 15; ?/? = 6;??? = 1;
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 ?15| 15?15 ? ?15| 15?15 ? ?? = 3(? ?)15|= 3 = 3 (1 + ?) ? ?15|+ 15?15= 0 ? = ?15| 15?15 TVM: ? = 15; ?/? = 6;??? = 1;
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 ?15| 15?15 ? ?15| 15?15 ? ?? = 3(? ?)15|= 3 = 3 (1 + ?) ? ?15|+ 15?15= 0 ? = ?15| 15?15 TVM: ? = 15; ?/? = 6;??? = 1;?? = 15;
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 ?15| 15?15 ? ?15| 15?15 ? ?? = 3(? ?)15|= 3 = 3 (1 + ?) ? ?15|+ 15?15= 0 ? = ?15| 15?15 TVM: ? = 15; ?/? = 6;??? = 1;?? = 15; CPT ??
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 ?15| 15?15 ? ?15| 15?15 ? ?? = 3(? ?)15|= 3 = 3 (1 + ?) ? ?15|+ 15?15= 0 ? = ?15| 15?15 TVM: ? = 15; ?/? = 6;??? = 1;?? = 15; CPT ?? (Result = numerator)
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 ?15| 15?15 ? ?15| 15?15 ? ?? = 3(? ?)15|= 3 = 3 (1 + ?)
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 ?15| 15?15 ? ?15| 15?15 ? ?? = 3(? ?)15|= 3 = 3 (1 + ?) TVM:
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 ?15| 15?15 ? ?15| 15?15 ? ?? = 3(? ?)15|= 3 = 3 (1 + ?) TVM: BGN
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 ?15| 15?15 ? ?15| 15?15 ? ?? = 3(? ?)15|= 3 = 3 (1 + ?) TVM: 15 N BGN FV
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 ?15| 15?15 ? ?15| 15?15 ? ?? = 3(? ?)15|= 3 = 3 (1 + ?) TVM: 15 N FV 6 I/Y BGN
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 ?15| 15?15 ? ?15| 15?15 ? ?? = 3(? ?)15|= 3 = 3 (1 + ?) TVM: 15 N FV 6 I/Y 1 +/- PMT BGN
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 ?15| 15?15 ? ?15| 15?15 ? ?? = 3(? ?)15|= 3 = 3 (1 + ?) PV TVM: FV 6 I/Y 1 +/- PMT CPT 15 N BGN
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 4.0360 ?15| 15?15 ? ?15| 15?15 ? ?? = 3(? ?)15|= 3 = 3 (1 + ?) PV TVM: FV 6 I/Y 1 +/- PMT CPT 15 N BGN
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 4.0360 ?15| 15?15 ? ?15| 15?15 ? ?? = 3(? ?)15|= 3 = 3 (1 + ?) PV TVM: FV 6 I/Y 1 +/- PMT CPT 15 N BGN .06
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 4.0360 ?15| 15?15 ? ?15| 15?15 ? ?? = 3(? ?)15|= 3 = 3 (1 + ?) PV TVM: FV 6 I/Y 1 +/- PMT CPT 15 N BGN .06 1.06
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 4.0360 ?15| 15?15 ? ?15| 15?15 ? ?? = 3(? ?)15|= 3 = 3 (1 + ?) PV TVM: FV 6 I/Y 1 +/- PMT CPT 15 N BGN .06 1.06 3
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 4.0360 ?15| 15?15 ? ?15| 15?15 ? ?? = 3(? ?)15|= 3 = 3 (1 + ?) PV TVM: FV 6 I/Y 1 +/- PMT CPT 15 N BGN = .06 1.06 3
???????? ??????? An annuity due with annual payments has an initial payment of 3. Each subsequent payment is 3 more than its preceding payment until reaching a final payment of 45. Determine the present value of the annuity using a 6% annual effective interest rate. 3 6 45 4.0360 ?15| 15?15 ? ?15| 15?15 ? ?? = 3(? ?)15|= 3 = 3 (1 + ?) PV TVM: FV 6 I/Y 1 +/- PMT CPT 15 N BGN = .06 1.06 3 ?? = 213.91
