Question

You receive payments at the end of each Quarter starting at the end of Quarter 1 and lasting 6 years (so the last payment you receive is at the end of Quarter 24). These payments are an equal series of payments of $1,000 for all 24 payment periods. The interest rate is 10% APR compounded monthly. What is the present value (at the beginning of Quarter 1) of this series of 24 payments?

Answer 1

Answer:

PV = PMT [(1 - (1 / (1 + r)ⁿ)) / r]

Where:

PV = The present value of the annuity

PMT = The amount of each annuity payment

r = The interest rate

n = The number of periods over which payments are to be made

PV = PMT [(1 - (1 / (1 + r)ⁿ)) / r]

     = 1000 [(1 - (1 / (1 + 0.0083)²⁴)) / 0.0083]

     = 1000 [(1 - (1 / 1.2194)) / 0.0083]

     = 1000 [(1 - 0.8201) / 0.0083]

     = 1000 [0.1799‬ / 0.0083]

     = 1000 * 21.6747

PV = $ 21,674.70

Explanation:

Since the annuity is compounded monthly

r = 10% / 12 = 0.83%

n = 24

Answer 2

Answer:

$17,843.78

Explanation:

Since the interest is compounded monthly and the payments are made once every 3 months (quarterly), we must do the calculations based on the monthly payment sequence:

$0; $0; $1,000; $0; $0; $1,000 ... $0; $0; $1,000 until we complete the 24 payments.

r = 10% / 12 = 0.83333%

We can use the excel NPV function = NPV(rate, values) =NPV(0.8333%,$0,$0,$1,000, etc.) we just select the 72 cells

= $17,843.78