Question

Wildhorse 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

Quarterly deposit= $9,508.68

Step-by-step explanation:

First, we need to calculate the future value of the initial investment:

FV= PV*(1+i)^n

PV= $168,000

i= 0.10/4= 0.025

n= 10*4= 40

FV= 168,000*(1.025^40)

FV= $451,090.73

Difference= 1,092,000 - 451,090.73= $640,909.27

Now, 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= (640,909.27*0.025) / [(1.025^40) - 1]

A= $9,508.68