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# Calculating the Periodic Payments for Given Cases

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1. What equal (uniform) series of payments must be put into a sinking fund to accumulate \$65000 in 15 years at 15% compounded annually when payments are annual?

2. What annual equal payment series is necessary to repay a series of 10 end-of-year payments that begins at \$6000 and decreases at a rate of \$200 a year with 12% interest compounded annually?

3. What is the present value of the geometric series with a first year base of \$15000 increasing at 10% per year to year 8 with an interest rate of 13%?

4. What equal annual amount must be deposited for 10 years in order to provide withdrawals of \$200 at the end of the second year, \$400 at the end of the third year, \$600 at the end of the fourth year, and so on, up to \$1800 at the end of the tenth year? The interest rate is 13% compounded annually.

5. Which of the following nominal interest rates provides the most interest over a year?
a. 19% compounded daily or 20% compounded annually?
b. 38% compounded monthly or 43% compounded annually?

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#### Solution Preview

1. What equal (uniform) series of payments must be put into a sinking fund to accumulate \$65000 in 15 years at 15% compounded annually when payments are annual?

Let the annual amount be R.
Rate of interest=i=15%
Number of periods=n=15
Future value of annuity=FV=\$65000
We know that FV of annuity is given by
FV=R*((1+i)^n-1)/i
65000 = R*((1+15%)^15-1)/15%=R*47.58041
R=65000/47.58041=\$1366.11

2. What annual equal payment series is necessary to repay a series of 10 end-of-year payments that begins at \$6000 and decreases at a rate of \$200 a year with 12% interest compounded annually?

Number of periods=n=10
Interest rate=i=12%