Question

Grouper Inc. wishes to accumulate $1,066,000 by December 31, 2030, to retire bonds outstanding. The company deposits $164,000 on December 31, 2020, which will earn interest at 8% 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 $1,066,000 is available at the end of 2030. (The quarterly deposits will also earn at a rate of 8%, compounded quarterly).

Answer 1

Quarterly deposit= $11,653.28

Step-by-step explanation:

First, we need to determine the future value of the lump sum investment. We need to use the following formula:

FV= PV*(1+i)^n

n= 10*4= 40 quarters

i= 0.08/4= 0.02

PV= $164,000

FV= 164,000*(1.02^40)

FV= $362,118.51

Now, the total difference to reach the $1,066,000:

Difference= 1,066,000 - 362,118.51= $703,881.49

To calculate the quarterly deposit, we need to use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= quarterly deposit

Isolating A:

A= (FV*i)/{[(1+i)^n]-1}

A= (703,881.49*0.02) / [(1.02^40) - 1]

A= $11,653.28