Suppose the interest rate is 9% APR with monthly compounding. Then the present value of an annuity that pays $250 every three months for the next five years is closest to:a.$4150.b.$2280.c.$3990.d.$3985.e.$3995.
Question
Suppose the interest rate is 9% APR with monthly compounding. Then the present value of an annuity that pays 4150.b.3990.d.3995.
Solution
The correct answer is a. $4150.
This is an annuity problem where we know the annuity payment (PMT), the interest rate (r), and the number of periods (n), and we want to find out the present value (PV).
The formula for the present value of an annuity is:
PV = PMT * [(1 - (1 + r)^-n) / r]
Since the interest rate is given as an annual rate and the payments are quarterly, we need to convert the interest rate to a quarterly rate: r = 9% / 4 = 0.0225. Also, since the payments are made for five years, the number of periods is 5 * 4 = 20 quarters.
Substituting the given values into this formula gives:
PV = $250 * [(1 - (1 + 0.0225)^-20) / 0.0225]
Calculating this gives a present value of approximately $4150.
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