Mia wants to save $8,000 for a down payment on a car. To the nearest dollar, how much will she need to invest in an account now with 7.9% APR, compounded daily, in order to reach her goal in 3 years?

Answer 1

We can use the formula for compound interest to solve this problem:

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

where:
A = the amount of money Mia will have after 3 years
P = the principal amount (the amount she needs to invest now)
r = the annual interest rate (7.9%)
n = the number of times the interest is compounded per year (365, since it's compounded daily)
t = the time in years (3)

Plugging in the values, we get:

A = P(1 + 0.079/365)^(365*3)
8000 = P(1 + 0.000216)^(1095)
8000 = P(1.229)
P = 8000/1.229
P ≈ $6,507.77

Therefore, Mia will need to invest approximately $6,507.77 in an account with 7.9% APR, compounded daily, in order to reach her goal of $8,000 in 3 years.