Question

Earl Ezekiel wants to retire in San Diego when he is 65 years old. Earl is now 52. He believes he will need $380,000 to retire comfortably. To date, Earl has set aside no retirement money. Assume Earl gets 10% interest compounded semiannually. How much must Earl invest today to meet his $380,000 goal? (Use the Table provided.) (Do not round intermediate calculations. Round your answer to the nearest dollar amount.)

a) $123,609
b) $128,834
c) $133,172
d) $138,626

Answer 1

Earl must invest approximately $128,834 today to meet his $380,000 goal. Option b is correct.

Step-by-step explanation:

To find out how much Earl must invest today to meet his $380,000 goal, we can use the formula for compound interest: A = P(1+r/n)^(nt).

A = the future value of the investment, which is $380,000.

P = the principal amount, which is what we need to find.

r = the annual interest rate, which is 10% or 0.10 in decimal form.

n = the number of times the interest is compounded per year, which is semiannually or 2 times per year.

t = the number of years, which is the difference between Earl's retirement age (65) and his current age (52), so t = 65 - 52 = 13 years.

Substituting these values into the formula, we get:

$380,000 = P(1+0.10/2)^(2*13)

Simplifying the equation:

$380,000 = P(1.05)^26

Dividing both sides of the equation by (1.05)^26:

P = $380,000 / (1.05)^26

Using a calculator, we find that P is approximately $128,834.

Therefore, Earl must invest approximately $128,834 today to meet his $380,000 goal. Option b is correct.