Question

An engineer wishes to have $3 million by the time he retires in 35 years. Assuming 8% nominal interest, compounded continuously, what annual sum must he set aside?

Answer 1

Answer:

annual sum must he set aside $16209.42

Explanation:

given data

engineer wishes = $3 million

retires time = 35 years

nominal interest = 8%

solution

we get here effective annual rate that is

interest rate  = $e^{r} - 1$  ...........1

interest rate  = $e^{0.08} - 1$

interest rate  = 0.08328 = 8.33%

and

now we get annual sum must he set aside that is

amount = $3 million × $\frac{rate}{(1+rate)^{t}-1}$

amount = $3000000 × $\frac{0.0832}{(1+0.0832)^{35}-1}$

amount = $16209.42