Question

Metlock Inc. wishes to accumulate $1,380,000 by December 31, 2027, to retire bonds outstanding. The company deposits $200,000 on December 31, 2017, which will earn interest at 6% 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 $1,380,000 is available at the end of 2027. (The quarterly deposits will also earn at a rate of 6%, compounded quarterly.)

Answer 1

Quarterly deposit= $18,743.98

Step-by-step explanation:

i= 0.06/4= 0.015

n= 10*4= 40

First, we need to determine the future value of the $200,000 using the following formula:

FV= PV*(1+i)^n

FV= 200,000*1.015^40

FV= $362,803.68

Now, we calculate the quarterly deposit to cover for the difference:

Difference= 1,380,000 - 362,803.68= $1,017,196.32

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

A= quarterly deposit

Isolating A:

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

A= (1,017,196.32*0.015) / [(1.015^40) - 1]

A= $18,743.98