Question

A perpetuity has end of month payments. The January payments are 1 , the February payments are 2, the March payments are 3 , the April payments are 4 , the May payments are 5 , the June payments are 6 , the July payments are 7 , the August payments are 8 , the September payments are 9 , the October payments are 10 , the November payments are 11 and the December payments are 12. The nominal rate of interest is 1.2% convertible monthly. Calculate the present value for the perpetuity.

Answer 1

To calculate the present value of the perpetuity with end of month payments, divide each payment by the interest rate and sum them up.

Step-by-step explanation:

To calculate the present value of the perpetuity, we need to use the formula:

PV = R / i

where PV is the present value, R is the payment amount, and i is the interest rate.

In this case, the January payment is 1, so the present value for January is 1 / 0.012 = $83.33. Similarly, the present values for February to December can be calculated using the corresponding payment amounts and the interest rate of 1.2%.

The sum of all the present values: PV = $83.33 + $166.67 + ... + $1000 = $5700