Question

Dubois Inc. wishes to accumulate $1,300,000 by December 31, 2022, to retire bonds outstanding. The company deposits $200,000 on December 31, 2012, which will earn interest at 10% compounded quarterly, to help in the retirement of this debt. In addition, the company wants to know how much should be deposited at the end of each quarter for 10 years to ensure that $1,300,000 is available at the end of 2022. (The quarterly deposits will also earn at a rate of 10%, compounded quarterly.) (Round to even dollars.)

Answer 1

Dubois Inc. must deposit $11,320 at the end of each quarter for 10 years

Explanation:

Given:

Present Value = $200,000

Future Value = $1,300,000

Payment = ? In question

N (time) = 40 (quarterly for 10 years)

I (Interest) = 2.5% (10% / 4 for quarterly)

Calculating the Future Value (FV)

FV = $200,000 * 2.5%^40

FV = $537,012

Calculating Additional Amount to earn

Amount = $1,300,000 - $537,012

Amount = $762,988

The corresponding future Value if annuity is 67.40255

Quarterly Deposit is then calculated as: $762,988 ÷ 67.40255

Quarterly Deposit = $11319.87

Quarterly Deposit = $11,320 ---- Approximated

Hence, Dubois Inc. must deposit $11,320 at the end of each quarter for 10 years