Question

"You need to have $15,000 in five years to pay off a home equity loan. You can invest in an account that pays 5.75 percent compounded quarterly. How much will you have to invest today to attain your target in five years? (Round to the nearest dollar."

Answer 1

I have to invest $11364.

Step-by-step explanation:

The formula of Compound Interest is:

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

where A = Amount

P = Principle

r = rate

n = Number of Compounding per year

t = total number of year

Here, A = 15000, r = 5.75% = 0.0575, n = 4(quarterly), and t = 5.

Putting all these values in above formula:

`15000 = P(1+(0.0575)/(4))^(4*5)`

⇒
`15000 = P((4.0575)/(4))^(20)`

⇒
`15000 = P(1.014)^(20)`

⇒
`15000 = P(1.320)}`

⇒ P = 11364

Hence, I have to invest $11364 for 5 years.