Question

In: Finance

Nancy would like to accumulate $10,000 by the end of 3 years from now to buy...

Nancy would like to accumulate $10,000 by the end of 3 years from now to buy a sports car from her friend, Jim. She has $2,500 now and would like to save equal annual end-of-year deposits to pay for the car. How much should she deposit at the end of each year in an account paying 8 percent interest to buy the car?

Expert Solution

Step 1:

Compute the future value of amount that she has at present.

Future value of $2,500 after 3 years = Present value × [1 + (Interest rate / Number of compounding periods per year)]^{Number of compounding periods per year ×
Time in years}

= PV × (1 + r / n)^{n × t}

= $2,500 × [1 + (0.08 / 1)]^{1 × 3}

= $2,500 × (1.08)³

= $2,500 × 1.259712

= $3,149.28

Step 2:

Compute the future value of an ordinary annuity as follows-

Future value of annuity = The amount required to be accumulated after 3 years - Future value of $2,500 after 3 years

= $10,000 - $3,149.28

= $6,850.72

Step 3:

Compute the required annual deposit at the end of each year using the equation given below-

Annual deposit = Future value of an ordinary annuity / [{(1 + r)ⁿ – 1} / r]

= $6,850.72 / [{(1 + 0.08)³ – 1} / 0.08]

= $6,850.72 / 3.2464

= $2,110.25

Hence, the she should deposit $2,110.25 at the end of each year to buy the car.

jeff jeffy answered 7 months ago

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