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?

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Business

Mohammad Davidson

9 June, 07:48

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?

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Joy · Answer 1

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