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# Applications of TVM concepts

1. What is the present value of \$2000 a year for 10 years at 12% compounded annually?

2. What series of equal (uniform) payments is necessary to repay the following present amounts?
a. \$500 in 5 years at 10% compounded annually with annual payments?
b. \$10000 in 15 years at 10% compounded annually with annual payments.

3. What annual equal (uniform) payment series is necessary to repay a series of 30 end-of-year payments that begins at \$250 and increases at the rate of \$50 a year with 9% interest compounded annually?

4. Find the nominal annual interest rate and effective interest rate per compounding period for the following effective annual interest rate: 18.39%, monthly compounding.

#### Solution Preview

1. In this case Annual payment=A=\$2000
Number of years=n=10
Interest rate=i=12%
Present value of given annuity=A*(P/A, i, n)=2000*P(P/2000, 12%,10)
(P/A, i, n)= 1/i*(1-1/(1+i)^n)=1/12%*(1-1/(1+12%)^10)= 5.65022
Present value of given annuity=2000*5.65022=\$11,300.44

2.a) \$500 in 5 years at 10% compounded annually with annual payments?
Number of periods=n=5
Interest rate=10%
Present value of loan=P=\$500
We have to find annual payments ...

#### Solution Summary

Time value of money concepts play an important role in making financial decisions. Solutions to given problems apply TVM concepts. There are four problems. Solutions to these problems depict the methodology to find present value, uniform cash flow and nominal interest rate. Calculations are carried out with the help of suitable formulas.

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