Question

a. What is the future value of 20 periodic payments of $4,720 each made at the beginning of each period and compounded at 8%?

b. Robert Finley wishes to become a millionaire. His money market fund has a balance of $111,780 and has a guaranteed interest rate of 10%. How many years must Robert leave that balance in the fund in order to get his desired $752,000?

Answer 1

a.Future value of annuity due=(1+rate)*Annuity[(1+rate)^time period-1]/rate

=1.08*4720[(1.08)^20-1]/0.08

=4720*49.4229214

=$233276.19(Approx)

b.We use the formula:  
A=P(1+r/100)^n
where   
A=future value
P=present value  
r=rate of interest
n=time period.

752,000=111,780*(1.1)^n

(752,000/111,780)=(1.1)^n

Taking log on both sides;

log (752,000/111,780)=n*log 1.1

n=log (752,000/111,780)/log 1.1

=20 years