Problem Assignment: Time Value of Money 1 If you deposit $15,000 today and earn

Question

Problem Assignment: Time Value of Money

1 If you deposit $15,000 today and earn 8% annual interest, how much will you have in 9 years?


2 Tiffany will receive a graduation gift of $10,000 from her parents in 3 years. If the discount rate
is 7%, what is this gift worth today?


3 What is the present value of a 20-year ordinary annuity of $30,000 using a 6% discount rate?


4 You deposit $5,000 in an account that pays 8% interest per annum. How long will it take to double your money?


5 The Johnsons have $60,000 to use as a down-payment on a house, and they want to borrow $240,000
from the bank. The current mortgage interest rate is 5%. If they make equal monthly payments for 30 years,
how much will the monthly payment be?


6 Tim paid $250 per month into his 401K retirement plan. After 30 years, he had accumulated $500,000. What
average annual rate of interest had he earned over the 30 years?


7 Charlotte's firm had sales of $525,000 in the year 2001. By 2012, sales had increased to $1,200,000. What was
the average annual rate of increase?


8 Alan had saved up $252,000. How much more must he save each year over the next 20 years in order to have a
total of $1 million? Alan earns 5% interest, compounded annually.

Explanation / Answer

1 If you deposit $15,000 today and earn 8% annual interest, how much will you have in 9 years? = 15000(1+0.08)^9 = 29985.06941 answer 2 Tiffany will receive a graduation gift of $10,000 from her parents in 3 years. If the discount rate is 7%, what is this gift worth today? = 10000/1.07^3 = 8162.978769 answer 3 What is the present value of a 20-year ordinary annuity of $30,000 using a 6% discount rate? PV = 30000{(1+0.06)^20-1)}/0.06 = 1103567.736 asnwer 4 You deposit $5,000 in an account that pays 8% interest per annum. How long will it take to double your money? 10000 = 5000(1+0.08)^n 5 The Johnsons have $60,000 to use as a down-payment on a house, and they want to borrow $240,000 from the bank. The current mortgage interest rate is 5%. If they make equal monthly payments for 30 years, how much will the monthly payment be? 6 Tim paid $250 per month into his 401K retirement plan. After 30 years, he had accumulated $500,000. What average annual rate of interest had he earned over the 30 years? 7 Charlotte's firm had sales of $525,000 in the year 2001. By 2012, sales had increased to $1,200,000. What was the average annual rate of increase? = (1200000- 525000)/525000*100 = 128 = 128/5 = 25.7% answer 8 Alan had saved up $252,000. How much more must he save each year over the next 20 years in order to have a total of $1 million? Alan earns 5% interest, compounded annually. 748000 = A({1-(1+0.05)^-20}/0.05 A = 60021.45522 answer

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