A person wishes to have $21,900 cash for a new car 3 years from now. How much should be placed in an account​ now, if the account pays 4.9% annual interest​ rate, compounded​ weekly?

Question

A person wishes to have $21,900 cash for a new car 3 years from now. How much should be placed in an account​ now, if the account pays 4.9% annual interest​ rate, compounded​ weekly?

$ ______ (round to nearest dollar)

Answer 1

The basic equation for compound interest is A(t) = A₀(1+r/n)^nt where A(t) is the amount available at any time "t" where "t" is measured in years, A₀ is the initial amount (at time t = 0), r is the interest rate (annual), and n"n" is the compounding periods. So:

21900 = A₀(1 + 0.049/52)^52•3

21900 = A₀(1.000942308)¹⁵⁶

21900 = 1.158273845A₀

A₀ = 21900/1.158273845 = $18,907.45

Answer 2

Assuming 52 weeks in a year, weekly interest rate will be (4.9 / 52) %

3 years = 3 x 52 weeks = 156 weeks

So if the amount placed now is A

A ( 1 + (4.9 / 5200))^ 156 = 21900

A = 21900 / 1.158273789 = $ 18907. 45 to nearest cent