Question

	Payment Years Interest Rate (Annual) Future Value (Payment made on last day of period) Future Value (Payment made on first day of period) $283 15 15 % 6,155 10 12 76,084 7 14 168,932 11 5

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))

Answer 1

Future value (Payment made on last day of period):

Future value of annuity is calculated as C*(((1+r)^n)-1)/r; where C is the annual cashflow, r is the discount rate and n is the number of years.

For the payment of $283,
Future value= 283*(((1+15%)^15)-1)/15%= $13465.26

For the payment of $6155,
Future value= 6155*(((1+12%)^10)-1)/12%= $108012.46

For the payment of $76084,
Future value= 76084*(((1+14%)^7)-1)/14%= $816418.71

For the payment of $168932,
Future value= 168932*(((1+5%)^11)-1)/5%= $2399980.97

Future value (payment made on first day of period):

Future value of annuity due is calculated as (1+r)*C*(((1+r)^n)-1)/r; where C is the annual cashflow, r is the discount rate and n is the number of years

For the payment of $283,
Future value= 283*(((1+15%)^15)-1)/15%= $15485.04

For the payment of $6155,
Future value= 6155*(((1+12%)^10)-1)/12%= $120973.96

For the payment of $76084,
Future value= 76084*(((1+14%)^7)-1)/14%= $930717.32

For the payment of $168932,
Future value= 168932*(((1+5%)^11)-1)/5%= $2519980.02