You can afford monthly deposits of $190 into an account that pays 3.3% compounded monthly. How long will it be until you have $8,900 to buy a​ boat?

Question

You can afford monthly deposits of $190 into an account that pays 3.3% compounded monthly. How long will it be until you have $8,900 to buy a​ boat?

Type the number of​ months: _________

​(Round to the​ next-higher month if not​ exact.)

Answer 1

Let us use the future value formula to solve:

FV = PV(1 + r/n)^nt

FV = future value

PV = present value

r = interest rate

n = number of times compounded

Now let's solve for t:

FV/PV = (1 + r/n)^nt

ln(FV/PV) = nt * ln(1 + r/n)

nt = ln(FV/PV)/ln(1 + r/n)

t = ln(FV/PV)/(n * ln(1 + r/n))

Now plug in the values:

t = ln(8900/190)/(12 * ln(1 + 0.033/12))

t = 116.74 = 117 months