Question

Suppose a man invested $300 at the end of 1900 in each of three

funds that tracked the averages of stocks, bonds, and cash,
respectively. Assuming that his investments grew at the rates
given in the table to the right, approximately how much would
each investment have been worth at the end of 2010?
Category
Stocks
Bonds
Cash
His investment in the fund tracking stocks would be worth approximately $
(Do not round until the final answer. Then round to two decimal places as needed.)
Average Annual Return
6.4%
1.7%
0.7%

Answer 1

To calculate the value of each investment at the end of 2010, we need to use the compound interest formula:

A = P(1 + r/n)^(nt)

where:

A = the final amount

P = the initial investment

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

For the investment in the fund tracking stocks:

P = $300

r = 6.4% = 0.064

n = 1 (assuming the interest is compounded annually)

t = 2010 - 1900 = 110

A = 300(1 + 0.064/1)^(1*110) = $208,884.78 (rounded to the nearest cent)

For the investment in the fund tracking bonds:

P = $300

r = 1.7% = 0.017

n = 1

t = 2010 - 1900 = 110

A = 300(1 + 0.017/1)^(1*110) = $2,326.34 (rounded to the nearest cent)

For the investment in the fund tracking cash:

P = $300

r = 0.7% = 0.007

n = 1

t = 2010 - 1900 = 110

A = 300(1 + 0.007/1)^(1*110) = $862.38 (rounded to the nearest cent)

Therefore, the investment in the fund tracking stocks would be worth approximately $208,884.78 at the end of 2010, the investment in the fund tracking bonds would be worth approximately $2,326.34, and the investment in the fund tracking cash would be worth approximately $862.38.