Aaron invests $3,500 initially and increases his investments at a rate of 10% pe

Question

Aaron invests $3,500 initially and increases his investments at a rate of 10% per year for 10 years. That is, Aaron has 11 total investments. If the future value of Aaron's investments (i.e., at the time of his last investment) equals $89,251, the Ror earned by Aaron is closest to...

Answer is 7.5. I just need to figure out how to work it out without excel

10. Aa Aaron has 11 total investments. If the future value of Aaron's investments (i.e., at the time of his last investmen equals $89,251, the ROR earned by Aaron is closest to ron invests $3,500 initially and increases his investments at a rate of 10% per year for 10 years. That is a) 5.0% b) 7.5% 9.2% d) 10.3% e) 11.4% f) 16.2% g) 17.7% ,2? ?,

Explanation / Answer

10.

Correct Answer:

B.7.5%

Working note:

Let, the rate of return = R

Total FV = $89251

Deposits at the end of first year = 3500*(1+10%) = $3850

So,

FV = FV of the initial deposit of $3500 + FV of increasing annuity

FV = 3500*(1+R)^10 + 3850*((1+R)^10-(1+10%)^10)/(R-.1)

At R = 7%

Future value of total deposits = $87297.55

At R = 8%

Future value of total deposits = 91258.60

So,

R = 8% - ((91258.60-89251)/( 91258.60-87297.55))*(8%-7%)

R = 7.49% or 7.5%

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