Question

Assume the total cost of a college education will be $235,000 when your child enters college in 18 years. You presently have $53,000 to invest. What annual rate of interest must you earn on your investment to cover the cost of your child’s college education? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

A = $235,000

P = $53,000

n = 1 because it was compounded once in a year.

t = 18 years

Therefore,.

235000 = 53000(1 + r/1)^1 × 18

235000/53000 = (1 + r)^18

4.43 = (1 + r)^18

Raising both sides to the power of 1/18, it becomes

4.43^(1/18) = (1 + r)^18 × 1/18

1.086 = 1 + r

r = 1.086 - 1

r = 0.086

r = 0.086 × 100 = 8.6%