Question

Question1) An engineer invests a lump sum of $56,000 today and wants to create a retirement fund worth $1 million in 40 years. What average annual rate of return is needed to accomplish this goal? Round your answer to three significant figures.

Question2) A firm borrows $300,000 to be repaid with 5 annual payments of $45,000 and a final balloon payment of $170,000. What is the average annual interest rate for this loan? Express your answer as a percentage, but do not include a percent sign. Round your answer to three significant digits. (solve without spreadsheet functions)

Answer 1

Answer (1)

We will use present value factor to calculate the annual rate of return.

$PV=\frac{FV}{(1+r)^{n}}$

$56,000=\frac{1000,000}{(1+r)^{40}}$

On solving we get-

$r=7.472$

ANSWER (2)

We will use ( Net Present Value=0) concept

$CASH_{outflow}-CASH_{inflow}=0\Rightarrow CASH_{outflow}=CASH_{inflow}$

we start from time t=0 years

$\frac{300,000}{(1+r)^{0}}=\frac{45,000}{(1+r)^{1}}+\frac{45,000}{(1+r)^{2}}+\frac{45,000}{(1+r)^{3}}+\frac{45,000}{(1+r)^{4}}+\frac{45,000}{(1+r)^{5}}+\frac{170,000}{(1+r^{5})}$

on solving we get-

$r=7.546$