Question

How much must you deposit today if you can earn 2.40% annual rate of interest (with monthly compounding) in order to have $42,000 seven years from now? Please show ALL work with finance formulas.

Answer 1

For compound interest, we have

A = P*(1+r)^n

Where, A = Amount received = 42000

P = principal = ?

r = rate of interest = 2.40 % per year = 2.4/12% per month(as compounded monthly) = 0.2 % per month = 0.002

n = period = 7 years = 7*12 months = 84 months

Thus,

42000 = P*(1+0.002)^84

42000 = P * 1.002^84

P = 42000 / (1.002^84)

P = 35510.8

Thus, you must deposit $35,510.8 today if you can earn 2.40% annual rate of interest (with monthly compounding) in order to have $42,000 seven years from now.