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Time Value of Money

1) Will annual payments of $4800 be sufficient to repay a loan of $40,000 in 20 years of an interest rate of
10% compounded annually?
10% compounded continuously?
12% compounded quarterly?

2) Maintenance costs for a new piece of mining equipment are expected to be $20,000 in the first year, rising by $1,000 per year thereafter. The machine has an expected life of 8 years and interest is 10% annually. To evaluate bids from outside firms for a maintenance contract you need to know the present value of these costs. What is this value?
In question 8 if the maintenance costs rose by 6% per year instead of the fixed amount what is the present value of the maintenance costs?

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Please see the attached file.

1) Will annual payments of $4800 be sufficient to repay a loan of $40,000 in 20 years of an interest rate of
10% compounded annually?
10% compounded continuously?
12% compounded quarterly?

We have to calculate the present value of $ 4800 payments at different interest rates and compare it with the loan amount.
Since we have annual payments we first calculate the effective annual interest rates for different compoundings
Present value of annuity (in this case annual payments) = PVIFA (r%, n years) x Annual amount
PVIFA = Present value interest factor for annuity
PVIFA =( 1- 1/(1+r)^n)/r
(^ means raised to the power of)
Loan amount= $40,000

10% compounded annually?
n= 20 years
r= effective annual rate = 10%
Annual Payments= $4,800

PVIFA (10.%, 20 years ) = 8.5136 =(1-(1/(1+10.%)^20))/10.%
Therefore, present value of annual payments= $40,865.28
Since this amount is more than the loan amount ($40,000), it is sufficient

10% ...

Solution Summary

Answers 2 Time Value of Money questions

$2.19