Question

The present value of a perpetuity paying 15 at the end of every 4-year period, with the first payment made at the end of year 4 , is 37.50. Using the same annual effective interest rate, find the present value of a perpetuity paying 1 at the end of each 4-month period, with the first payment made at the end of 4 months.

A 30.98
B 35.17
C 36.17
D 41.47
E 47.05

Answer 1

B. 35.17

Explanation:

You want the present value of a perpetuity paying 1 at the end of each 4-month period, given the interest rate is the same effective rate as that of a perpetuity with a present value of 37.50 paying 15 at the end of each 4-year period.

Interest rate

The payment of a perpetuity is equal to the interest earned in the period. If the interest earned on a present value of 37.50 is 15 in 4 years, then the value multiplier for 4 months will be ...

(1 +15/37.50)^(1/12) . . . . . . . 12 4-month periods in 4 years

≈ 1.02844 = 1 +r

Interest earned

If the interest earned in 4 months is 0.02844 of the present value, and the interest earned is 1, then the present value is ...

I = Pr

P = I/r = 1/0.02844 = 35.17

The present value of the perpetuity paying 1 every 4-month period is 35.17.