Question

  Amy and Vince want to save

​$5,000

so that they can take a trip to Europe in four years. How much must they save each month to have the money they need if they can get 5​%,

compounded​ monthly, on their​ savings?

Answer 1

Future value annuity is used to calculate the value of a series of periodic payments at a future date with a given interest rate.
The payment at each interval can be calculated with the below formula:

P = [FV*r/m] / [(1+r/m)^m*ⁿ -1]
where P = Periodic payment
FV = future value or value to be saved at the end of the period
n = no. of periods, here n = 4 years
m = compounding period = 12 months.
r = rate of 5%.
= [5000*0.05/12] / [( 1+0.05/12)^12*4-1]
=[20.8333] / [(1+ 0.004167)⁴⁸-1]
= 20.8333 / [1.220895 - 1]
= $94.31

Amy and Vince need to save $94.31 every month to save $5000 in the next four years at a rate of 5% compounded monthly.

answered by: anonymous