# Calculating the Periodic Payments for Given Cases

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?

#### 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%

Gradient=G=-$200

Present value of given annuity=A *(P/A,12%,10)+G*(P/G,12%,10)

In this case, the annuity of withdrawals starts with 6000, and G=-$200

(P/A,I,n)= ...

#### Solution Summary

Time Value of Money concepts play an important role in financial decision making. Solutions to the given problems use present value formulas for ordinary annuity, annuity with geometric progression and annuity with arithmetic progression to find out the periodic cash flows. The response also compare interest rates with different compounding and select the beneficial options.