Question

Larkspurn wishes to 400.000 by December 2007. The 3000 Dec 2017, wi places, 5512) t h the

Larkspur Inc. wishes to accumulate $1,400,000 by December 31, 2027, to retire bonds outstanding. The company deposits $200,000 on December 31, 2017, 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 9 years to ensure that $1,400,000 is available at the end of 2027. (The quarterly deposits will also earn at a rate of 10%, compounded quarterly.) (Round answer to 0 decimal places, e.g. 458,582.)

Answer 1

The formula for compound interest, including principal sum, is:
A = P (1 + r/n) ^(nt)

Where:

• A = the future value of the investment/loan, including interest
• P = the principal investment amount (the initial deposit or loan amount)
• r = the annual interest rate (decimal)
• n = the number of times that interest is compounded per unit t
• t = the time the money is invested or borrowed for

1. If company deposits $ 200,000 on 31 December,2017

A = 200000 (1 + 10/4) ^ (4*10)

A = 200000 (1 + 2.5) ^ 40

A = 200000 (3.5) ^ 40

A = 200000 * 5.790576

A = $11,58,115

2. If Company wishes to accumulate $14,00,000 by 31 December,2027

$14,00,000 = P (1+10/4) ^ (4*10)

$14,00,000 = P ( 1+2.5) ^ 40

$14,00,000 = P * 5.790576

P = $14,00,000/5.790576

P = $ 2,41,772

Answer 2

Future Value of $200,000 Deposit

Formula: 
FV=PV(FVFn,i)

FV=$200,000(FVF40,2.5%)

FV=$200,000*(2.68506) <factor list
FV=537,012

Amount to which quarterly deposits must grow:

$1,400,000-$537,012 =$862,988

Annuity of the value of quarterly deposits

Formula:

FV-OA=R(FVF-OAn,i)

$862,988=R(FVF-OA40,2.5%)

$862,988=R(67.40255) <factor list)

R=$862,988/67.40255

R=$12,803