An investment of $6000 at the start of the year will pay $1000 at the end of the year for a set number of years.What is the minimum number of years these payments must be made for if the investment is to be worthwhile,given that the interest rate is 6%?
A)6 years
B)7 years
C)8 years
D)9 years
E)10 years

Question

Quizplus · Accepted Answer

To determine whether the investment is worthwhile, we need to calculate the future value of the investment at the end of the payment period. Using the formula for future value of an annuity:

FV = PMT x [(1 + r)^n - 1]/r

Where FV is the future value, PMT is the payment amount, r is the interest rate, and n is the number of payment periods.

Plugging in the numbers, we get:

$6000 = $1000 x [(1 + 0.06)^n - 1]/0.06

Simplifying, we get:

6 = (1.06^n - 1)/0.06

Multiplying both sides by 0.06, we get:

0.36 = 1.06^n - 1

Adding 1 to both sides, we get:

1.36 = 1.06^n

Taking the natural log of both sides, we get:

ln(1.36) = n x ln(1.06)

Dividing both sides by ln(1.06), we get:

n = ln(1.36)/ln(1.06) = 8.16

Since the number of payment periods has to be a whole number, the minimum number of years needed to make the investment worthwhile is 8 years (option C).

An Investment of $6000 at the Start of the Year