1. Assume you just deposited $8,500 into an account that earns interest of 6% pe

Question

1. Assume you just deposited $8,500 into an account that earns interest of 6% per year, compounded annually. How many years will it take for your balance to reach $10,000?

2. I plan to deposit $250 into an account at the end of each month. The account earns 5% per year, compounded monthly. How many months will it take for my balance to reach $25,000?

3. In 1980, a gallon of gas cost $1.08. According to AAA, the national average was $2.22 per gallon in 2016. What was the average annual inflation rate in the price of gas?

4. You are evaluating an investment. It promises to pay you $1,000 one year from today, $2,000 two years from today, and $3,000 three years from today. If you require a rate of return of 9% on the investment, what is the most you would be willing to pay for it today?

5. Suppose you have been offered the opportunity to invest in a start-up business. The owners have asked you to invest $15,000 today. Based on their forecasts, they expect that your investment will be worth $40,000 in 7 years. What annual rate of return does this imply?

Explanation / Answer

1.

PV = FV/(1+r)^n

PV - Present value

FV - Future value

r - Interest rate

n - no. of periods

8500 = 10000/(1+0.06)^n

n = log(10000/8500)/log(1.06) = 2.79 years.

2.

FV of annuity = P*[((1+r)^n - 1)/r]
P - Periodic payment = 250
r - rate per period = 0.05
n - number of periods = ?

25000 = 250*(((1+0.05)^n - 1)/0.05)

n = 36.72 months.

3.

PV = FV/(1+r)^n

n = 2016-1980 = 36years

1.08 = 2.22/(1+r)^36

r = 0.0202 = 2.02%

4.

PV = 1000/(1+0.09)^1 + 2000/(1+0.09)^2 + 3000/(1+0.09)^3 = 4917.34

PV = $4917.34

5.

15000 = 40000/(1+r)^7

r = 0.1504 = 15.04%

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