Question

Q1. Calculating Interest Rates

Assume the total cost of a college education will be $345,000 when your child enters college in 18 years. You presently have $73,000 to invest. What annual rate of interest must you earn on your investment to cover the cost of your child’s college education?

Q2. Calculating the Number of Periods

At 6.1 percent interest, how long does it take to double your money? To quadruple it?

Answer 1

Answer to Question 1:

Current Balance = $73,000
Desired Balance = $345,000
Time Period = 18 years

Current Balance * (1 + Interest Rate)^Time Period = Desired Balance
$73,000 * (1 + Interest Rate)^18 = $345,000
(1 + Interest Rate)^18 = 4.726027
1 + Interest Rate = 1.0901
Interest Rate = 0.0901 or 9.01%

Answer to Question 2:

Part 1:

Amount Invested = $1
Desired Sum = $2
Interest Rate = 6.10%

Amount Invested * (1 + Interest Rate)^Time Period = Desired Sum
$1 * (1 + 0.0610)^Time Period = $2
1.0610^Time Period = 2
Time Period * ln(1.0610) = ln(2)
Time Period = 11.71 years

Part 2:

Amount Invested = $1
Desired Sum = $4
Interest Rate = 6.10%

Amount Invested * (1 + Interest Rate)^Time Period = Desired Sum
$1 * (1 + 0.0610)^Time Period = $4
1.0610^Time Period = 4
Time Period * ln(1.0610) = ln(4)
Time Period = 23.41 years