SOLUTION: You are the vice president of finance for a manufacturer of scuba diving gear. The company is planning a major plant expansion in 5 years. You have decided to start a sinking fund

Question 1172796: You are the vice president of finance for a manufacturer of scuba diving gear. The company is planning a major plant expansion in 5 years. You have decided to start a sinking fund to accumulate the funds necessary for the project. Your company's investments yield 12% compounded quarterly. It is estimated that $3,000,000 in today's dollars will be required; however, the inflation rate on construction costs and plant equipment is expected to average 6% per year for the next 5 years.
A) Use the compound interest concept to determine how much (in $) will be required for the project, taking inflation into account.
B) What sinking fund payments (in $) will be required at the end of every 3-month period to accumulate the necessary funds?
For A, I used the compound interest formula of compound amount - principal. I got 1,040,580 and 2,418,330. Both answers were wrong.
For B, I used the sinking value formula: future value x i/(1+i)^n-1. My answers were 129,737.21 and 111,647.12

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you didn't say that either of your answers for B were correct or incorrect.
let me give it a shot.

for A, the question is:

A) Use the compound interest concept to determine how much (in $) will be required for the project, taking inflation into account.
inflation rate on construction costs and plan equipment is expected to average 6% per year for the next 5 years.
3,000,000 * 1.06^5 = 4,014,676.733 in 5 years.
because of inflation, the costs increase by 6% per year.

for B, the question is:

B) What sinking fund payments (in $) will be required at the end of every 3-month period to accumulate the necessary funds?

i used a financial calculator to answer this question.
what i got was:
the quarterly payment to the fund would have to be 149,409.04 dollars.

my inputs were:
present value (pv) = 0
future value (fv) = 4,014,676.733
number of time periods (np) = 5 years * 4 quarters per year = 20 quarters.
interest rate % per time period (ir) = 12% per year / 4 = 3% per quarter.
payment is made at the end of each time period (beginning/end).

i then clicked on payment amount (pmt) and it told me that the amount of money to be invest at the end of each quarter is 149,409.04, as stated above.

i then looked at your formula.
that formula is for future value, not for payments.
so, to begin with, you used the wrong formula.
the formula i have is in the following reference.
https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#formulas
the particular formula from that reference is shown below:

ANNUITY FOR A FUTURE AMOUNT WITH END OF TIME PERIOD PAYMENTS
a = (f*r)/((1+r)^n-1)
a is the annuity.
f is the future amount.
r is the interest rate per time period.
n is the number of time periods.

in this formula, you use the rate per quarter, not the percent rate per quarter.

with a future amount of 4,014,676.733 (without the commas), and an interest rate of .03 per quarters and a number of time periods of 20, the formula becomes:

a = (f*r)/((1+r)^n-1) becomes:
a = (4014676.733 * .03) / ((1+.03)^20-1)
solve to get:
a = 149409.0354

round that to 2 decimal places and it becomes 149409.04, same as i got with the financial calculator.

the results from the financial calculator are shown below:

let me know if these answers get you to the right answer.
i'll be very happy if they do.
i'll be most interested in finding out what the correct answer is so i can figure out where i went wrong if they don't.

theo

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