Question

You have $12,500 you want to invest for the next 30 years. You are offered an investment plan that will pay you 7 percent per year for the next 10 years and 9.5 percent per year for the last 20 years. How much will you have at the end of the 30 years?

Answer 1

Answer:

Balance after 30 years = $151,018.50

Explanation:

In order to calculate this, we will calculate the future value on an amount invested, gaining interest over the years of investment, and this is given by:

$FV = PV (1 + r)^{t}$

where:

FV = future value

PV = present value

r = interest rate

t = time in years.

Hence the future value is calculated as follows:

1. For the first 10 years at 7% interest:

7% interest = 7/100 = 0.07

$FV = 12,500 (1 + 0.07)^{10}$

$FV = 12,500 (1.07)^{10}\\FV = 12,500 * 1.967 = 24,589.392$

2. For the last 20 years at 9.5%(0.095) interest:

Note that for the remaining 20 years, the present value (PV) used = 24,589.392, as ending balance after the first 10 years

$FV = 24,589.392 (1 + 0.095)^{20}$

$FV = 24,589.392 (1.095)^{20}\\FV= 24,589.392 * 6.1416\\FV = 151,018.496$

Total Future value earned = $151,018.50