Question

Reagan has a savings account that earns 1.87% interest, compounded quarterly. If she needs $20,857 for a down payment on a house in 9 years, how much money will she need to invest in the account today?

A. 10,704.95
B. 17,633.17
C. 19,355.32
D. 20,508.99

Answer 1

To solve this, we are going to use the compounded interest formula:
`A=P(1+ (r)/(n) )^(nt)`
where

`A` is the final amount after
`t` years

`P` is the initial investment

`r` is the interest rate in decimal form

`n` is the number of times the interest is compounded per year

`t` is the time in years

We know from our problems that she needs $20,857 for a down payment on a house in 9 years, so
`A=20857` and
`t=9`. To convert the interest rate to decimal form, we are going to divide the rate by 100%

`r= (1.87)/(100) =0.0187`
Since the interest is compounded quarterly, it is compounded 4 times per year; therefore,
`n=4`.
Lets replace the values in our formula to find
`P`:

`A=P(1+ (r)/(n) )^(nt)`

`20857=P(1+ (0.0187)/(4) )^((4)(9))`

`P= (20857)/((1+ (0.0187)/(4) )^((4)(9)))`

`P= (20857)/((1+ (0.0187)/(4) )^(36))`

`P=17633.17`

We can conclude that the correct answer is: B. 17,633.17