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# Time Value of Money

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1. John Smith has received a \$1,000,000 gift from his grandmother. Below are two alternatives for investment. Calculate the current value of each. Which investment should John choose and why?

A. Invest in a one year government security yielding 5%.
B. Invest in real estate with some risk. John has found a piece of property for \$1,000,000 that is forecasted to be worth \$1,100,000 after one year.

2. Tom Jones is 65 years of age and has a life expectancy of 12 more years. He wishes to invest \$20,000 in an annuity that will make a level payment at the end of each year until his death. If the interest rate is 8%, what income can Mr. Jones expect to receive each year?

3. Evaluate the three investment opportunities for bonus of \$1,000 you just received. Find the values at 1 year, 5 years, and 20 years. Indicate which opportunity is the best for each of time periods.

A. An account paying 12% interest compounded annually.
B. An account paying 11% interest compounded semi-annually.
C. An investment that will pay you 14% annual interest only at the end of the investment period. of 1 year, 5 years, or 20 years.

## SOLUTION This solution is FREE courtesy of BrainMass!

1. John Smith has received a \$1,000,000 gift from his grandmother. Below are two alternatives for investment. Calculate the current value of each. Which investment should John choose and why?
A. Invest in a one year government security yielding 5%.
Return= 5%

B. Invest in real estate with some risk. John has found a piece of property for \$1,000,000 that is forecasted to be worth \$1,100,000 after one year.

Return= 10% = (\$1,100,000 / \$1,000,000)-1

John can choose either of the two investments depending on his risk tolerance.
If he wants a less risky investment, he can choose a government security that has a lower return.
If he can tolerate risk, he can choose real estate. He will be rewarded by a higher return (10%) for taking this risky investment.

2. Tom Jones is 65 years of age and has a life expectancy of 12 more years. He wishes to invest \$20,000 in an annuity that will make a level payment at the end of each year until his death. If the interest rate is 8%, what income can Mr. Jones expect to receive each year?

We have to calculate annuity

n= 12
r= 8.00%
PVIFA (12 periods, 8. % rate ) = 7.536078

Present value= \$20,000
Therefore, annuity= \$2,653.90 =20000/7.536078

(PVIFA= Present value interest factor for an annuity)

Answer: Income that Mr. Jones can expect to receive each year= \$2,653.90

3. Evaluate the three investment opportunities for bonus of \$1,000 you just received. Find the values at 1 year, 5 years, and 20 years. Indicate which opportunity is the best for each of time periods.

We have to calculate Future Value of a sum of money
FVIF= Future Value Interest Factor

A. An account paying 12% interest compounded annually.

Amount= \$1,000
Interest= 12%

No of years= Frequency No of Periods Discount rate annually Discount rate per period FVIF Future Value
1 A 1 12.00% 12.0000% FVIF (1 periods, 12.% rate ) = 1.12 \$1,120.00 =1000x1.12
5 A 5 12.00% 12.0000% FVIF (5 periods, 12.% rate ) = 1.762342 \$1,762.34 =1000x1.762342
20 A 20 12.00% 12.0000% FVIF (20 periods, 12.% rate ) = 9.646293 \$9,646.29 =1000x9.646293

No of years= Value=
1 \$1,120.00 \$1,120.00
5 \$1,762.34 \$1,762.34
20 \$9,646.29 \$9,646.29

B. An account paying 11% interest compounded semi-annually.

Amount= \$1,000
Interest= 11%

No of years= Frequency No of Periods Discount rate annually Discount rate per period FVIF Future Value
1 S 2 11.00% 5.5000% FVIF (2 periods, 5.5% rate ) = 1.113025 \$1,113.03 =1000x1.113025
5 S 10 11.00% 5.5000% FVIF (10 periods, 5.5% rate ) = 1.708144 \$1,708.14 =1000x1.708144
20 S 40 11.00% 5.5000% FVIF (40 periods, 5.5% rate ) = 8.513309 \$8,513.31 =1000x8.513309

No of years= Value=
1 \$1,113.03 \$1,113.03
5 \$1,708.14 \$1,708.14
20 \$8,513.31 \$8,513.31

C. An investment that will pay you 14% annual interest only at the end of the investment period. of 1 year, 5 years, or 20 years.

Amount= \$1,000
Interest= 14%

No of years= Future value
1 \$1,140.00 =1000x(1+1 x 0.14)
5 \$1,700.00 =1000x(1+5 x 0.14)
20 \$3,800.00 =1000x(1+20 x 0.14)

Investment in A is the best

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