Question

Bridgeport Inc. wishes to accumulate $1,092,000 by December 31, 2030, to retire bonds outstanding. The company deposits $168,000 on December 31, 2020, 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 $1,092,000 is available at the end of 2030. (The quarterly deposits will also earn at a rate of 10%, compounded quarterly.) (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.)

Answer 1

Answer: $9,479

Explanation:

The number of periods = 10 years * 4 quarters = 40 periods

Interest per quarter = 10%/4 = 2.5%

$168,000 has been deposited. The value of this cash after 10 years is;

= 168,000 ( 1 + 2.5%) ^ 40

= $451,090.72

Out of $1,090,000, the amount remaining is;

= $1,090,000 - 451,090.72

= $638,909.28‬

They need to deposit an annuity per quarter to get to $638,909.28‬.

Future Value of Annuity = Annuity * ([1 + I]^N - 1 )/I

638,909.28‬ = Annuity * [(1+0.025)^40 - 1] /0.025

638,909.28 = Annuity * 67.40255

Annuity = 638,909.28/67.40255

= $9,479