Continuous compounding

Question

How much must be deposited today into the following account in order to have $40,000 and 6 years for a downpayment on a house.? As soon no additional deposits are made. An account with a monthly compounding and an APR of 8%  $_______ should be deposited today.

Answer 1

This is not a continuous compounding problem; It is monthly compounding. You are given the future value of a single investment that earns interest compounded monthly You can solve the problem using a formula, a spreadsheet function, compound interest tables, or a financial calculator. The calculator is simplest, but you still have to understand how compounding works. The interest rate is annual so you have to convert it to a monthly rate The formula is

 

PV = FV / (1 + r/t)^nt where r is the annual rate, t 12 months per year, n is the number of years. In this problem you have

 

PV = 40,000 / (1.06667)^6*12

 

PV = 24,790.79

 

Using a financial calculator you input:

 

FV = 40,000

N = 6*12 = 72

i% = 8/12 = .66667%

PMT = 0 -- this variable is used for annuities.

PV = ?