Suppose there is no inflation,and the current interest rate is 4% per year.Erin plans to open a savings account and deposit $100 annually for the next 5 years.She plans to leave this money untouched for 10 more years.At the end of the period,the balance of her savings account will be

Question

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First, we need to determine the future value of each annual deposit of $100 for the next 5 years, at 4% interest rate, compounded annually:

FV5 = 100(1 + 0.04)^5 = $122.02

Next, we need to determine the future value of the total savings after 5 years, at 4% interest rate, compounded annually:

FVA5 = 122.02(1 + 0.04)^5 - 1)/0.04 = $638.15

Then, we need to determine the future value of this amount after an additional 10 years, at 4% interest rate, compounded annually:

FVA15 = 638.15(1 + 0.04)^10 = $867.41

Finally, we need to add the value of the 5 annual deposits of $100 that Erin will make during the 10-year period, at 4% interest rate, compounded annually:

FV15 = 867.41 + 100[((1 + 0.04)^10 - 1)/0.04] = $2504.95

Therefore, the balance of Erin's savings account at the end of the period will be $2504.95, which corresponds to choice D.

Suppose There Is No Inflation,and the Current Interest Rate Is