Question

FUTURE VALUE OF AN ORDINARY ANNUITY
FVOA= A(FVAF) PVOA=(PVAF)

We will only be concerned with ordinary annuities, where the same payments are made or received at the end of each time period.

Just remember payments can be made at the beginning of the period, called annuities due, the calculation used is slightly different .

1. Piper opens up an IRA and places the maximum contribution of $5,500 in her retirement account at the end of each year for 20 years. She believes the account will earn 11 percent interest per year, compounded annually.   

1. How much will she have in her retirement account in 20 years?

2. What if the interest rate is only 8%? How much will she have in her retirement account in 20 years?

2. Fairview Corp. borrows $4 million by issuing bonds. It plans to set up a sinking fund that will repay the loan at the end of 10 years. Assume a 5 percent interest rate per year. What should the company place into the fund at the end of each year to have $4 million in the account to pay back their bondholders?  

Hint: This is a future value of an ordinary annuity problem. You will solve for “A”

3. You just had a baby and want to get started on a college fund for your child. You figure you will need $120,000 available in 18 years. You believe you can earn an annual rate of 9% on your money. How much would you have to set aside at the end of year to have $120,000 in 18 years?

4. Jorge plans to retire at the age of 65 and believes he will live to be 85. He wants to receive an annual retirement payment of $50,000 at the end of each year. He sets up a retirement account that is estimated to earn 8 percent annually.
   1. How much money must Jorge have in the account when he reaches reach 65 years old?

2. Jorge is currently 30 years of age. How much must he invest in this account at the beginning of each year for the next 35 years to have the amount you just calculated (in 4.a) in his account at age 65?

Hint - This is then a future value of an ordinary annuity and you are solving for “A”.

5. XTRA CREDIT PROBLEM: Calculate the monthly mortgage payment made on a $120,000 mortgage. The mortgage is for fifteen years and the interest rate is 4 percent

Answer 1

As per rules I am answering the first 4 subparts of the question

Q No
1	Amount in account	$353,115.58
2	Amount in account	$251,690.80
3	Amount to be deposited at the end of each year	$318,018.30
4	Amount to be deposited at the end of each year	$2,905.47

WORKINGS