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How to calculate the future value compounded weekly?

Find the amount (future value) of an ordinary annuity of $120 per week for 6.5 years at 8.3% per year compounded weekly. (Round your answer to the nearest cent.)

I tried this problem a few times, but I just can't seem to get the right answer.

=$53709.98

(I need help to setting up the...

# How to calculate the future value compounded weekly?

Find the amount (future value) of an ordinary annuity of $120 per week for 6.5 years at 8.3% per year compounded weekly. (Round your answer to the nearest cent.)

I tried this problem a few times, but I just can't seem to get the right answer.

=$53709.98

(I need help to setting up the problem).

I tried this problem a few times, but I just can't seem to get the right answer.

=$53709.98

(I need help to setting up the problem).

## 5 Answers

- 00
- If P is the present value, and i is the interest per period, and n is the number of periods, then the future value F of a single payment made today is: F = P(1+i)^n. Since interest is usually expressed in annual terms, the annual rate would be divided by 52 before being used in this formula. The number of weeks would be n. If you are talking about the future value of a stream of payments, beginning today, then: F = P((1+i)^n -1)/i00
- The same question pops up again00
- Compounded Weekly00
- The weekly interest, r, paid on the account is 0.083/52 ≈ 0.001596153846. The total number of compounding periods, n, is 52 (6.5) = 338, and the weekly payment into the annuity is $120.

The formula for the sum of an annuity is this:

S = a [(1 + r)^n - 1]/ (r), where a is the periodic payment made to the annuity, r is the periodic interest rate, and n is the total number of compounding periods in which the annuity grows. Plugging in the values, we get this:

S ≈ $120 [(1.001596153846)^338 - 1]/(0.001596153846)

S ≈ $120 (1.714411534 - 1)/(0.001596153846)

S ≈ $120 (0.714411534 / 0.001596153846)

S ≈ $120 (447.5831298)

S ≈ $53,709.97557 which rounds to S ≈ $53,709.98.00

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