Question

A perpetuity pays $23 at the beginning of every month forever. The present value of this perpetuity is $4623. Calculate the nominal annual rate of interest compounded monthly earned by this perpetuity.

a) 3%
b) 4%
c) 5%
d) 6%

Answer 1

The nominal annual rate of interest compounded monthly earned by this perpetuity is 6%.

Step-by-step explanation:

To calculate the nominal annual rate of interest compounded monthly earned by this perpetuity, we can use the present value formula. The present value of the perpetuity is given as $4623. The monthly payment is $23. We can use the formula:

PV = C / r

Where PV is the present value, C is the monthly payment, and r is the nominal annual rate of interest compounded monthly. Substituting the given values:

$4623 = $23 / r

Rearranging the equation to solve for r:

r = $23 / $4623 = 0.005 (or 0.5%)

Multiplying by 12 to get the nominal annual rate:

0.005 * 12 = 0.06 (or 6%)

Therefore, the nominal annual rate of interest compounded monthly earned by this perpetuity is 6%.