Question

Show the work with formulas step by step please.

- How many years will it take for $100,000 to grow to $500,000 if it is invested at an annual interest rate of 9.15%? Round to the nearest 0.01.

- You are told that if you invest $5,000 per year for 35 years you will have accumulated $1,000,000. What is the annual rate of return on the latter investment? Round to the nearest 0.01%.

Answer 1

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

500,000=100,000*(1.0915)^n

(500,000/100,000)=(1.0915)^n

Taking log on both sides;

log 5=n*log (1.0915)

n=log 5/log (1.0915)

=18.38 years(Approx)

b.Putting into financial calculator;

FV=1,000,000

N(time period)=35

Annuity payment(PMT)=$5000

Solving for I/Y;we get;

I/Y=annual rate of return=8.67%(Approx)