Question Details

MATH 500 Week 7 Discussion

Annuities and Loan Payments 
Use the Annuity Calculator as appropriate to help answer the following questions. Be sure to work through the examples in the lecture first. You can access the Annuity Calculator from either the lecture, or with this link: Annuity Calculator
1.	Suppose Mary deposits $200 at the end of each month for 30 years into an account that pays 5% interest compounded monthly.

a.	How much total money will she have in the account at the end?

b.	How much total money did Mary actually deposit?

c.	How much total interest did the account earn over that period?

d.	Suppose instead of making monthly deposits, Mary decides to deposit a “lump sum” into the account. How much must she deposit? What is this value also called?

2.	Suppose a retiree wants to buy an ordinary annuity that pays her $2,000 per month for 20 years. If the annuity earns interest at 3.5% interest compounded monthly, what is the present value of this annuity?

3.	Suppose a student wants to be a millionaire in 40 years. If she has an account that pays 8% interest compounded monthly, how much must she deposit each month in order to achieve her goal of having $1,000,000? What is the present value of this annuity?

4.	Suppose John sells his house and earns a profit of $600,000. With the profit, he buys a 20 year annuity that earns 6.5% interest compounded monthly. What monthly payment will John get?

5.	You wish to purchase a house for $200,000 with 20% down. You will have it financed over 30 years at a rate of 8%. In addition, your yearly real estate tax is $4,800 while your monthly insurance payment on the home will be $30. What is your monthly mortgage payment? How much does your house cost per month including principal, interest, real estate taxes, and insurance?