   Chapter 5.1, Problem 52E

Chapter
Section
Textbook Problem

TRUST FUNDS A young man is the beneficiary of a trust fund established for him 21 years ago at his birth. If the original amount placed in trust was $10 , 000 , how much will he receive if the money has earned interest at the rate of 6% / year compounded annually? Compounded quarterly? Compounded monthly? To determine The amount that the young man will earn from the trust fund when it is compounded annually, when compounded quarterly and when compounded monthly. Explanation Given: The fund invested was$10000.

The interest rate is 6%/year compounded monthly.

Time period is 21years.

Approach:

The expression of the accumulated amount.

A=P(1+rm)t×m...(1)

Here, A is the accumulated amount, P is the principal amount, r is the interest rate, t is the time period in years and m is the number of periods per year.

Calculation:

Calculate the present worth of the trust fund when compounded annually.

The period per year is,

m=1

Substitute $10000 for P, 6% for r, 21years for t and 1 for m in equation (1) to solve for A. A=$10000(1+0.061)(21×1)=$10000(3.399563601)=$33995.64

Calculate the present worth of the trust fund when compounded quarterly.

The period per year is,

m=4

Substitute \$10000 for P, 6% for r, 21years for t and 4 for m in equation (1) to solve for A

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