# Annuity Calculations

If not explicitly stated always assume payments are made at the end of the period.

1.The Derr-McGee Manufacturing Company plans to build a new $50,000 warehouse seven years from now. They plan to accumulate the $50,000 in an account before beginning construction. If money is worth 7% compounded annually, how much must each year?s deposit be in order to accumulate $50,000 at the end of the seventh year?

2.The Johnson family plans to purchase a new home five years from now. How much will they have accumulated in a savings account if they deposit $500 at the end of every six months for five years? The savings account earns interest at the rate of 5 % compounded semi-annually.

3.The XYZ Television Company offers a machine for $200 down and $25 per month for one year. If interest is charged at 18% compounded monthly, find the actual cash value of the television.

4.Sam Jones plans to retire at age 65. He wants to supplement his retirement by buying an annuity that will provide $2,400 each year for 10 years. If money is worth 8% compounded annually, how much will Jones have to pay for the annuity at age 65?

5.Marie Richard purchases a new sports car for $35,500. What is the monthly payment if Marie agrees to pay for the car in 48 months if the car dealer is offering an interest rate of 6.5% APR? Marie wishes to pay off the loan completely after one year of monthly payments. How much would this lump sum payment be?

6.A loan of $10,000 at 10% compounded annually is being amortized over 6 years. Under the following headings, work at the first four lines of the amortization schedule using annual payments and determine the outstanding principal after the fourth payment has been made.

Payment Numb Annual Payment Int Portion Principal Reduction Outstanding

1.

2.

3.

4.

7.Sally contributed $500 every six months for fourteen years into an RRSP earning interest at 7.5% compounded semi-annually. Seven years after the last contribution Sally converted the RRSP into an RRIF which is to pay her equal quarterly payments for sixteen years. If the first payment is due three months after the conversion into the RRIF and the interest on the RRIF is 9% compounded quarterly, how much will Sally receive every three months?

8.Mr. Strupp expects to retire in 12 years. Beginning one month after his retirement, he would like to receive $500 per month for twenty years. How much must he deposit into a fund today to be able to do so if the rate of interest on the deposit is 12% compounded monthly?

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#### Solution Preview

Please refer attached file for better clarity of tables.

Solution:

1.The Derr-McGee Manufacturing Company plans to build a new $50,000 warehouse seven years from now. They plan to accumulate the $50,000 in an account before beginning construction. If money is worth 7% compounded annually, how much must each year?s deposit be in order to accumulate $50,000 at the end of the seventh year?

Number of periods=n=7

Periodic Payment=R=?

Future Value of ordinary annuity=S=$50000

Interest rate per period=i=7%

Future value of ordinary annuity is given by

S=R/i*((1+i)^n-1)

50000=R/7%*((1+7%)^7-1)=R*8.654021

R=50000/8.654021=5777.66

They should deposit $5777.66 per year to have a $50000 at the end of seven years

2.The Johnson family plans to purchase a new home five years from now. How much will they have accumulated in a savings account if they deposit $500 at the end of every six months for five years? The savings account earns interest at the rate of 5 % compounded semi-annually.

Number of periods=n=5*2=10 (half years)

Rate of interest=i=5%/2=2.5% per period

Periodic Payment R=R=$500

Future Value of annuity=S=?

Future value of ordinary annuity is given by

S=R/i*((1+i)^n-1)

=500/2.5%*((1+2.5%)^10-1)

=$5601.69

3.The XYZ Television Company offers a machine for $200 down and $25 per month for one year. If interest is charged at 18% compounded monthly, find the actual cash value of the television.

Number of periods=n=1*12=12

Interest rate=i=18%/12=1.5% per month

Periodic Payment=$25

PV of ordinary annuity is given by

PV=R/i*(1-1/(1+i)^n)

PV=25/1.5%*(1-1/(1+1.5%)^12)=$272.69

Actual cash value of Television=Down Payment+ PV of ordinary annuity

=200+272.69=$472.69

4.Sam Jones plans to retire at age 65. He wants to ...

#### Solution Summary

There are eight problems. Solutions to these problems explain methodology to find present value and future value of ordinary annuities. Solutions also explain the steps to determine equated periodic payments and amortization schedule of a loan.

Calculations for an ordinary annuity vs an annuity due

CASE AMOUNT OF ANNUITY INTEREST RATE DEPOSIT PERIOD (YR)

A $2,500 8% 10YRS

B 500 12 6

C 30,000 20 5

D 11,500 9 8

E 6,000 14 30

a. CALCULATE THE FUTURE VALUE OF THE ANNUITY ASSUMING THAT IT IS

1. An ordinary annuity

2. An annuity due

b. Compare your findings in a(1) and a (2). All else identical, which type of annuity - ordinary or annuity due - is preferable? Please explain why.