Partl: Future Value A payment of$200 is made at the end of each month into an ac
ID: 3148293 • Letter: P
Question
Partl: Future Value A payment of$200 is made at the end of each month into an account paying a 7.5% annual interest rate, compounded monthly for 30 years. a. What is the future value of the account after 30 years? b. How much did you put into the account? c. How much interest did you earn? A payment of S200 is made at the end of each month into an account paying an 8% annual interest rate, compounded monthly for 30 years. d. What is the future value of the account after 30 years? e. How much did you put into the account? f How much interest did you earn? Notice that the interest rate increased by only 0.5%. How much more interest did you earn from the 8% interest rate verses the 7.5% interest rate? I Are you surprised at this figure? Why or why not?Explanation / Answer
Future Value of annuity = Periodic Payment * ((1+ periodic interest rate)^number of periods)) - 1)/ Periodic interest rate
a
Future Value of annuity = $200 * ((1+ 0.075/12)^12*30)- 1)/0.075/12 = $269489.085
b
Amount Put in account = $200 * 360 = $72000
c
Interest earned = Future Value of annuity - Amount put in account = $269489.085 - $72000 = $197489.085
d
Future value of Annuity = $200 * ((1+ 0.08/12)^12*30)- 1)/0.08/12 = $298071.89
e
Amount put in account = $200 * 360 = $72000
f
Interest earned = Future Value of annuity - Amount put in account = $298071.89 - $72000 = $226071.89
Interest earned from 8% is $28582.80 more than that earned from 7.5%.
Not surprised as interest on the increasing deposit is getting compounded monthly for 30 years so the difference in amount of interest also has to be significant