Question

You want to purchase a new car in 7 years and expect the car to cost ​$77 comma 000. Your bank offers a plan with a guaranteed APR of 5.5 % if you make regular monthly deposits. How much should you deposit each month to end up with ​$77 comma 000 in 7 ​years?

Answer 1

Answer: $753.58

Explanation: The best way to calculate this is by using a financial calculator. An HP10bII+ is an appropriate financial calculator to use, although other financial calculators should still compute the same answer.

By using a financial calculator to find the answer the following elements are required:

Present Value (PV): the value of money currently that will grow into more money in the future. Because you still have to start saving money to deposit into the bank from the first month, your present value is still $0.

Interest rate (I/YR): the amount, in percentage terms, charged by the bank to you on the value of the money you deposited into the bank. This allows your deposit to grow on a month to month basis. In this case the bank charges an APR of 5.5%.

Number of years (N): the amount of years the money will stay in the bank before it matures. The value will grow over the next 7 years.

Future Value (FV): This is the final amount of a current investment after it has grown in an account that accrues interest over time. In this case it is the expected $77,000 at the end of the 7th year.

All the above elements are computed to find the payment per month (PMT). This is the amount of money you have to deposit into the account every month to receive a total future value of $77,000 after 7 years.

When these figures are inputed into a calculator the following outcome is deduced:

Ensure 12 periods per year (12 shift P/YR on calculator), as deposits are made every month for 12 months every year.

PV = 0

I/YR = 5.5%

N= 84 periods (i.e. 7 years x 12 months per year)

FV = $77.000

∴ PMT = $753.5766 rounded to $753.58 (ignore the minus sign, this only indicates that you are taking money out to deposit into the account monthly)