A family plans to save for a down payment on a condo by depositing $5,000 at the end of every year into a savings account that pays 6% APR, compounded annually.

The family intends to make 10 deposits (Year 1 to Year 10).

How much money will they have in the account immediately after your 10th deposit?

Round your final answer to the nearest cent. Enter two decimals, without punctuation e.g. enter 2500.35 for $2,500.3531

Question

A family plans to save for a down payment on a condo by depositing $5,000 at the end of every year into a savings account that pays 6% APR, compounded annually.

The family intends to make 10 deposits (Year 1 to Year 10).

How much money will they have in the account immediately after your 10th deposit?

Round your final answer to the nearest cent. Enter two decimals, without punctuation e.g. enter 2500.35 for $2,500.3531

BlackTom AI · Accepted Answer

The problem describes depositing 5,000 at the end of each year for 10 years into an account that earns 6% interest compounded annually. This is a standard ordinary annuity growth scenario.

To find the value immediately after the 10th deposit, use the future value of an ordinary annuity formula: FV = PMT × [((1 + r)^n − 1) / r], where PMT is the periodic payment, r is the periodic interest rate, and n is the number of deposits.

Here, PMT = 5,000, r = 0.06, and n = 10. Compute (1 + r)^n = 1.06^10. One way to do this is to note 1.06^5 ≈ 1.3382255776, and then square to get 1.06^10 ≈ 1.3382255776^2 ≈ 1.790847696. Subtract 1 to get 0.790847696.

Next, divide by r: 0.790847696 / 0.06 ≈ 13.18079493. This factor represents how many times the 5,000 payment effectively grows over the 10-year period.

Finally, multiply by PMT: 5,000 × 13.18079493 ≈ 65,903.97465. Rounding to the nearest cent yields 65,903.97.

Interpretation: Each yearly deposit earns interest for the remaining years, and the sum of these growing deposits accumulates to the final amount after the 10th deposit. The result 65,903.97 reflects the combined effect of all deposits compounding at 6% annually.

Edge check: if r were smaller or n larger, the future value would be different in a nonlinear way due to compounding, but the formula used correctly accounts for the time value of money for an ordinary annuity. No additional adjustments are needed since deposits are made at year-end and interest is compounded annually.

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