Ken will receive a $5,000 annual payment from a family trust. This will continue until Ken in 30;...

Question:

Ken will receive a {eq}\$5,000 {/eq} annual payment from a family trust. This will continue until Ken in {eq}30 {/eq}; he is now {eq}20 {/eq}. Inflation averages {eq}4\% {/eq} and Ken's real MARR is {eq}8\% {/eq}. If the first payment is a year from now and a total of {eq}10 {/eq} payments are to be made, what is the present worth of his remaining income from the trust?

Inflation Rate:

In general terms, the inflation rate measures the rate at which the general price level for a given bundle of services and products rises between two different periods. It is measured as a percentage change.

Answer and Explanation: 1

The number of periods is 10 years (30 years - 20 years), the future value is 8%, the inflation rate is 4%, and the interest rate is 8%.

The present worth of the remaining income from the trust can be estimated as:

{eq}PV = FV * \frac{(1-(100+Inflation/100)^{period})}{inflation /100}\\ PV = 5,000 * \frac{(1-(100+4/100)^{-10})}{4/100}\\ PV = 5,000 * \frac{1-(1.04^{-10})}{0.04}\\\\ PV = 5,000 * (1-0.6756) / 0.04\\ PV = 5,000 * (0.3244) / 0.04\\ PV = 5,000 * 8.110896 {/eq}

PV = 40554.48

So, it can be stated that the present worth of Ken's remaining income from the trust is $40554.48


Learn more about this topic:

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How to Calculate the Present Value of an Annuity

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Chapter 8 / Lesson 3
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Learn how to find present value of annuity using the formula and see its derivation. Study its examples and see a difference between Ordinary Annuity and Annuity Due.


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