Find the savings balance after 18 months with an APR of 18% and monthly payments of $200

Answer 1

Assuming you begin saving when the account has no money, let's begin by keeping track of the 5 key variables for questions like this:

N (number of periods) = 18 months

I/YR (interest per period) = 18% APR (annual) / 12 months per year = 1.5% monthly

PV (present value) = $0 since you start with no money in the account

PMT (payment per period) = -$200 (note that the payment is negative because the $200 is leaving your wallet every month, not because the payment itself is negative)

FV (future value) = ? (we're solving for this!)

The first way to solve for the future value using these variables is to use a financial calculator. Just plug in all of the values above into their respective keys, then click on the FV key to find a future value of $4,097.88, which is the amount you'll have in the account after 20 years.

You can also solve a question like this in Excel by using the FV function. Click on any cell in the sheet and type =FV(1.5%, 18, -200) to find the same future value of $4,097.88 that we found before.

Answer: $4,097.88

Answer 2

You would have to calculate the savings balance after 18 months with an APR of 18% and monthly payments of $200, by utilizing a formula for the future value of an annuity:

FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)

Thus:

FV = future value P = payment amount r = annual interest rate n = number of times interest is compounded per year t = time in years

Therefore, we have:

P = $200 (monthly payment) r = 18% (annual interest rate) n = 12 (interest is compounded monthly) t = 18/12 = 1.5 (time in years)

Entering in these values:

FV = $200 * ((1 + 0.18/12)^(12*1.5) - 1) / (0.18/12) = $200 * ((1.015)^(18) - 1) / (0.015) ≈ $3,590.50

Therefore, you would have a savings balance after 18 months of approximately $4,097.88