SOLUTION: I cannot get this answer correct to save my life. Could someone please help me. Thank you very much. On September 8, Bert Sarkis joined a Christmas club. His bank will automatic

Question 248887: I cannot get this answer correct to save my life. Could someone please help me. Thank you very much.
On September 8, Bert Sarkis joined a Christmas club. His bank will automatically deduct $65 from his checking account at the end of each month and deposit it into his Christmas club account, where it will earn 6% interest. The account comes to term on December 1.
(a) Find the future value of the account, using an annuity formula. (Round your answer to the nearest cent.)
(b) Find the future value of the account, using the compound interest formula. (Round your answer to the nearest cent.)
(c) Find Bert's total contribution to the account.
(d) Find the total interest. (Round your answer to the nearest cent.)

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
bert joined the christmas club on september 8th.
65 dollars is deducted from his checking account at the end of every month and deposited into the christmas club account.
the christmas club account earns 6% interest a year.
the account comes to term on december 1.

here's how it works.

the annual interest rate is 6%.
the monthly rate is 6% / 12% = .5% / 100% = .005

the account starts at 0.
at the end of september the account has 65 dollars in it.
at the end of october the account has 65 * 1.005 + 65 = 130.325 dollars in it.
at the end of november the account has 130.325 * 1.005 + 65 = 195.976625 dollars in it.
on december 1st, the account has $195.98 in it.

your questions are:

(a) Find the future value of the account, using an annuity formula. (Round your answer to the nearest cent.)

See the bottom for how to solve this using the annuity formula.

(b) Find the future value of the account, using the compound interest formula. (Round your answer to the nearest cent.)

This was done up top when I provided you with the month by month details.

(c) Find Bert's total contribution to the account.

Bert's total contribution was 3 * 65 = $195.00

(d) Find the total interest. (Round your answer to the nearest cent.)

The total interest was $.98

the assumption is that the interest is an annual interest rate.

to convert that to monthly interest rate you have to divide it by 12.

SOLVING USING AN ANNUITY FORMULA

The formula you want is future value of a payment.

payments and annuities are terms that are sometimes used interchangeably.

future value of a payment formula is the same as future value of an annuity formula.

sometimes they call it future worth rather than future value.

that formula is:

FUTURE VALUE OF A PAYMENT

FV = future value
PMT = payment per time period
i = interest rate per time period
n = number of time periods

in your problem

FV = x
PMT = 65
i = .06 / 12 = .005
n = 3 (you make payments in september, october, and november)

this formula assumed end of time period payments.

your formula becomes

your answer becomes:

x = 195.976625

this round out to x = $195.98

I confirmed using a financial calculator.

the principal is number of payments times the payment = 3 * 65 = 195.

the interest is the future value of the payments minus the payments = 195.98 minus 195 = .98

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