1. Imagine that you have a $1,000 CD earning 5% interest (i = .05) indefinitely. a. What is the future value of this CD in 10 years? b. The CD earns $50 interest each year on the $1,000 principal, yet in ten years it will have earned more than $500 interest. Explain why

a. Future value is $1628.89

b. it earns interest on interest in 10 years as the investor never withdraws the interest.

explanation:

a. We have been given a perpetuity where an initial investment of $1000 earns an interest of 5% indefinitely  but we are now told to calculate the future value of this CD in 10 years which will be calculated using the future value formula which is

Fv depicts the future value of the investment

Pv is the present value of the CD which is $1000 initial investment

i is the interest rate earned on the CD which is 5%

n is the number of years of which the CD( cash derivative) is saved for which in this case is 10 years.

Therefore if we substitute these values on the above mentioned formula and solve for Fv :

Fv = $1000(1+5%)^10

Fv = $1628.89 (correct to two decimal places)

this will be what the investment is worth after 10 years.

b. As calculated above we know that the interest after 10 years is $1628.89-$1000= $628.89 which is more than $500 because it is compound interest and not simple interest as in 10 years there will not be a withdrawal of the interest made each year therefore interest is reinvested and earns its own interest as the principal amount now.

Fv = 1000(1+ 0.05)^10