Compute the future values of the following annuities first a

Compute the future values of the following annuities first assuming that payments are made on the last day of the period and then assuming payments are made on the first day of the period: (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))

Compute the future values of the following annuities first assuming that payments are made on the last day of the period and then assuming payments are made on the first day of the period: (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))

Solution

Payment Years Interest rate Future Value (Payment made on last day of period) Future Value (Payment made on first day of period) (Annual) $ 183 13 12% $ 5,129.33 $          5,744.85 5,155 8 11                           61,135.38            67,860.28 75,084 5 13                       4,86,564.64        5,49,818.04           1,67,932 9 4                     17,77,189.98      18,48,277.58 Workings: There are two types of annuity-(a) Annuity due and (b) Ordinary Annuity When payments are made at the beginning of period, is termed as annuity due and on the other hand if at the end of period is know as ordinary annuity. Future Value of Ordinary Annuity = (((1+i)^n)-1)/i Where, i Interest rate n Life in years Future Value of annuity due = ((((1+i)^n)-1)/i)*(1+i) Working: Future Value of annuity due of 1 in case of: $ 183 ((((1+0.12)^13)-1)/0.12)*(1+0.12)                              31.3926                 5,155 ((((1+0.11)^8)-1)/0.11)*(1+0.11)                              13.1640               75,084 ((((1+0.13)^5)-1)/0.13)*(1+0.13)                                 7.3227           1,67,932 ((((1+0.04)^9)-1)/0.04)*(1+0.04)                              11.0061 Future Value of annuity of: $ 183 $                     183 x                              31.3926 $      5,744.85                 5,155 $                 5,155 x                              13.1640        67,860.28               75,084 $               75,084 x                                 7.3227     5,49,818.04           1,67,932 $           1,67,932 x                              11.0061 18,48,277.58 Future Value of ordinary annuity of 1 in case of: $                 183 (((1+0.12)^13)-1)/0.12                              28.0291                 5,155 (((1+0.11)^8)-1)/0.11                              11.8594               75,084 (((1+0.13)^5)-1)/0.13                                 6.4803           1,67,932 (((1+0.04)^9)-1)/0.04                              10.5828 Future Value of annuity of: $                 183 $                     183 x                              28.0291 $      5,129.33                 5,155 $                 5,155 x                              11.8594        61,135.38               75,084 $               75,084 x                                 6.4803     4,86,564.64           1,67,932 $           1,67,932 x                              10.5828 17,77,189.98