# 2.2 Practice - Annuities

### On each, first identify as a Future Value annuity or Present Value annuity. Then answer the question.

**1)**

*How much money must you deposit now at 6% interest compounded quarterly in order to be able to withdraw $3,000 at the end of each quarter year for two years?*

Type

Present Value

Show Answer

PV=$22457.78

**2)**

*Suppose you invested $1000 per quarter over a 15 year period. If money earns an annual rate of 6.5% compounded quarterly, how much would be available at the end of the time period. How much is the interest earned?*

Type

Future Value

Show Answer

FV=$100,336.68

Interest

$40,336.68

**3)**

*A bank loans a family $90,000 at 4.5% annual interest rate to purchase a house. The family agrees to pay the loan off by making monthly payments over a 15 year period. How much should the monthly payment be in order to pay off the debt in 15 years?*

Type

Present Value

Show Answer

PMT=$688.49

**4)**Suppose you have selected a new car to purchase for $19,500. If the car can be financed over a period of 4 years at an annual rate of 6.9% compounded monthly, how much will your monthly payments be? How much of your first payment is interest? How much of your second payment is interest?Type

Present Value

Show Answer

PMT=$466.05

Interest From 1st PMT

$112.13

Interest from 2nd PMT

$110.09

**5)**Suppose you will need $12,000 in 3 years. How much must you invest per month in order to have $12,000 if money earns an annual rate 6% compounded monthly? How much of the $12000 is interest?Type

FV

Show Answer

PMT=$305.06

Interest

I=12000-36(305.06)=$1017.84

**6)**

*Suppose on your 21st birthday you begin making monthly payments of $500 into an account that pays 8% compounded monthly. If you continue the payments until your 51st birthday (30 years), how much money will be in the account? How much of it is interest?*

Type

FV

Show Answer

$745,179.72

Interest

745179.72-360(500)=$565,179.72

**7)**Suppose your parents decide to give you $10,000 to be put in a college trust fund that will be paid in equally quarterly installments over a 5 year period. If you deposit the money into an account paying 1.5%

**per quarter**, how much are the quarterly payments (Assume the account will have a zero balance at the end of period.) Hint: What is i?

what is i?

i=1.5%=0.015

Type

PV

Show Answer

PMT=$582.46

**8)**

*Suppose the parents of a child begin making quarterly payments of $1,000 into an account paying 7% compounded quarterly. Payments begin on the 10th birthday. How much will be available on the child’s*

**a) 15th**and**b) 21st birthday?**Type

FV

Answer 15th Birthday

$23,701.61

Answer 21st Birthday

$65453.15

**9)**

*How long will it take for monthly payments of $500 to have a future value of $100,000 if money earns 6% compounded monthly? You must solve this using the appropriate formula that will require logarithms.*

Type

FV

Show Answer

n=139 months

**10)**

*You finally found your dream home. It sells for $120,000 and can be purchased by paying 10% down and financing the balance at an annual rate of 9.6% compounded monthly.*

**a**) How much are your payments if you pay monthly for 30 years?

**b**) Determine how much would be paid in interest .

**c**) Determine the payoff after 100 payments have been made.

**d**) Change the rate to 8.4% and the time to 15 years and calculate the payment.

**e**) Determine how much would be paid in interest and compare with the previous interest. (to nearest dollar)

Type

PV

Show Answer a)

PMT=$916.01

Show Answer b)

I=$221,763.60

Show Answer c)

Payoff=$100,077.71

Show Answer d)

PMT=$1057.20

Show Answer e)

$139,468

**11)**

*Experts say that the baby boom generation (born 1946-1960) cannot count on a company pension or Social Security benefits to provide a comfortable retirement. It is recommended that they start to save regularly and early. Michael, a baby boomer, has decided to deposit $200 each month in an account that pays 7.2% compounded monthly for 20 years.*

**a**) How much money will be in the account at the end of the 20 years?

**b**) Suppose Michael has determined he needs to accumulate $130,000 from this annuity. What rate would achieve this goal (use graphs) ?

**c**) If he can not get the higher rate, what amount would his payments need to be in order to achieve the goal?

**d**) Suppose Michael cannot get the higher interest rate, nor increase his payments. How many months would he need to invest in order to achieve his goal? Use logs.

Type

FV

Show Answer a)

$106,752.47

Show Answer b)

8.78%

Show Answer c)

$243.55

Show Answer d)

266 months

**12)**

*A man purchased a home 10 years ago valued at $80,000. He paid 20% down payment and signed a 30-year mortgage at 6.6% APR compounded monthly. Today, the net market value of the house is $120,000. How much equity does the man have in the house today?*

Type

PV

Hint 1

Amount Financed = $64,000

Hint 2

Monthly Payment=$408.74

Hint 3

240 remaining payments

Hint 4

Find PV with PMT=408.74 and n=240

Loan Payoff

New PV=$54,391.91

Equity

120,000-54391.91=$65,608.09

### On the rest, I did not list the type.

**13) EQUITY:**

*The Jones family purchased a $150,000 home 14 years ago. They paid 10% down and financed the remaining balance over a 30 year period. Their annual interest rate is 4.8% compounded monthly and today’s market value of the home is $190,000. How much equity (nearest dollar amount) do the Jones have in their home?*

Show Answer

$95,203

**14)**

*Mr. Ray has deposited $150 per month into an ordinary annuity. After 14 years, the annuity is worth $85,000. What*

**annual rate**compounded monthly has this annuity earned during the 14 year period? Solve by graphing.Show Answer

r=1.253%

**15) Solving For Rate In A PV Problem**

*Suppose you want to buy a $20,000 automobile and pay it off in 60 monthly payments of $375 per payment. What is the annual interest rate that will allow you to pay the debt off in exactly 60 payments? Solve using a graphing calculator.*

Show Answer

4.735%

**16)**

*Marie has determined that she will need $5000 per month in retirement over a 30-year period. She has forecasted that her money will earn 7.2% compounded monthly. Marie will spend 25-years working toward this goal investing monthly at an annual rate of 7.2%. How much should Marie’s monthly payments be during her working years in order to satisfy her retirement needs?*Hint: Find how much Marie must have at retirement, then find the monthly payments to reach that goal.

First Part: PV

PV=$736,606.78

2nd Part: FV. Solve for PMT

PMT=$880.90

**16b)**

*What maximum amount could Marie withdraw each month so that her balance never decreases (nearest dollar)?*

Hint

Find interest earned for the first period of the $736,606.78

Show Answer

I=Prt=736606.78(0.072)(1/12)=$4420

Conclusion

If she only withdraws $4420 each month, her balance stays the same.