Question

Ayayai 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.

Answer 1

Quarterly deposit= $11,653.28

Step-by-step explanation:

Future Value= $1,066,000

Number of periods= 10*4= 40 quarters

Interest rate= 0.08/4= 0.02

First, we need to calculate the future value of the initial investment. Then, determine the difference required to reach the objective.

FV= PV*(1+i)^n

FV= 164,000*(1.02^40)

FV= $362,118.50

Difference= 1,066,000 - 362,118.5= $703,881.5

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= (703,881.5*0.02) / [(1.02^40) - 1]

A= $11,653.28