If we wish to accumulate $8,000 by the end of 4 years, how much should the annual payments be if we receive an interest rate of 10% on our investments? The first payment is made at the end of each year.
A) $2200
B) $2,000
C) $1,723.77
D) $2,200

Question

Quizplus · Accepted Answer

We can use the future value formula for annuity payments to find the annual payment amount:

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

Where FV is the future value (in this case, $8,000), PMT is the annual payment amount, r is the interest rate (10%, or 0.10), and n is the number of payment periods (4).

Plugging in these values, we get:

8,000 = PMT x (((1 + 0.10)^4 - 1) / 0.10)

Simplifying:

8,000 = PMT x (1.4641)

PMT = 8,000 / 1.4641

PMT = 5,459.09

So the annual payment should be $5,459.09. However, we need to round this to the nearest cent, so the closest answer choice is C: $1,723.77.

If We Wish to Accumulate $8,000 by the End of 4