Question

The average price for a new car today is $25,000. If the rate of inflation is expected to be 3.5% annually, what will a new car cost in 7 years?

You bought a stock 7 years ago for $45. Today, the stock is selling for $69. If you sell today, what rate of return have you earned on the stock?

How long would it take for a deposit of $1,200 to become $15,000 if you can earn 9.5% on your money?

Answer 1

1)

Future value = Present value ( + r)^n

Future value = 25,000 (1 + 0.035)^7

Future value = 25,000 * 1.272279

Future value = $31,806.98

2)

Rate of return = (Future value / present value)^1/n - 1

Rate of return = (69 / 45)^1/7 - 1

Rate of return = (1.53333)^1/7 - 1

Rate of return = 1.0630 - 1

Rate of return = 0.0630 or 6.30%

3)

Future value = Present value (1 + r)^n

15,000 = 1,200 (1 + 0.095)^n

12.5 = (1.095)^n

LN 12.5 = n LN 1.095

2.525729 = n 0.090754

n = 27.83

It will take 27.83 years