1. (Compound Interest) A little Babie Duckie plans to buy a $225 rotisserie oven to roast itself in 5
years when it grows up. The Duckie finds a bank that pays quarterly compounded interest.
(a) If the bank is willing to offer an interest rate of 7.5%, how much money does the Duckie have to
invest now in order to afford the rotisserie oven 5 years later?
(b) Assume the bank only offers quarterly compounded interest. If the Duckie only has $140 now,
what annual interest rate must it get in order to accumulate enough money to place the purchase 5
years later?

Question

1. (Compound Interest) A little Babie Duckie plans to buy a $225 rotisserie oven to roast itself in 5 
years when it grows up.  The Duckie finds a bank that pays quarterly compounded interest. 
(a) If the bank is willing to offer an interest rate of 7.5%, how much money does the Duckie have to 
invest now in order to afford the rotisserie oven 5 years later? 
(b) Assume the bank only offers quarterly compounded interest.  If the Duckie only has $140 now, 
what annual interest rate must it get in order to accumulate enough money to place the purchase 5 
years later?

jamesj · Answer

What kind of cruel world is it where ducks buy the ovens in which they will be roasted?  What a bizarre way to set up this question.

Anyway.  How much is $1 invested now worth in 5 years if the interest rate is 7.5% and the interest is compounded quarterly?

jamesj · Answer

One dollar will be worth
$$ (1 + 0.075/4)^{5 \times 4} $$
Given that how much do you need to invest now to have $225 in the future?  Suppose P is invested now, what's the formula for P?