The amount of money in a bank account earning interest rate i for t years, having started with p dollars in principal, is:
For example: $100 earning 5% interest for 7 years would become:
1. George Washington put $1.00 in the Continental Bank in 1776. The account has paid 5% interest all these years. How much is in the bank account this year?
2. Mom and Dad are having a baby. They want to start a college fund. They want to put some money in an account earning 8% interest, so that when their child is 18 there will be $10,000 in the account. How much should they put in the account?
An annuity is an account (such as an IRA) in which you deposit some money every year. The account pays interest on whatever money is already in the account. The amount of money s in the account after n years of depositing r dollars every year, while earning an interest rate of i is:
For example: had I started an IRA in 1980, and put in $2000 every year, earning 8% interest for the ensuing 16 years until now, my IRA would have
Too bad I didn't start my IRA until 1995!!
3. If you started an IRA when you turned 21, and deposited $2,000 into it every year, earning 8% interest, how much money would be in the account when you retired at the age of 65?
4. Assume the same situation as in problem #3 above. But now you want to have $1,000,000 in your IRA when you retire at age 65. How much should you deposit into your IRA every year?
When you retire, you will want to start taking money out of your retirement account. If you take out too much money each year, you will run out of money. If you take out too little, you will leave the rest to your ungrateful children. The money remaining in your retirement account will continue earning interest.
The formula to determine the amount of money w you can withdraw each year
for n years if your account starts with p dollars and continues to earn
an interest
rate of i is:
For example, if my retirement account has $100,000 in it, earning 8% interest, and I plan on making my money last for 20 years:
5. If your IRA has $250,000 in it when you retire, and will earn an interest rate of 5%, how much money can you withdraw each year if you plan on making your money last for 25 years?
6. Assume the same situation as in problem #5 above. But now you want to be able to withdraw $25,000 each year for 20 years. How much money needs to be in your retirement account when you retire?
The monthly payment on a mortgage of a dollars at a monthly interest rate of i for m months is
For example: a $90,000 loan for 30 years at 9% annual interest would require a monthly payment of
Keep in mind that this monthly payment does not include taxes or insurance. Also don't forget that m is months, not years (multiply by 12), and that i is the monthly interest rate, not the annual interest rate (divide by 12).
7. What is the monthly mortgage payment for a $100,000 loan at an annual interest rate of 9% over 30 years?
8. Before I bought my house, I paid $435 per month in rent. What is the largest mortgage I could afford with an equivalent mortgage payment, assuming an annual interest rate of 8% over 30 years?
A zero-coupon bond is a kind of loan where the borrower does not make any monthly payments. Instead, the entire loan is paid off at the end of the loan period. Investors buy and sell these bonds. Many retirement finds also invest in bonds.
The price of a bond can be determined by rearranging the compound interest formula you used in the first two problems. The cost of bond that will pay m dollars in n years with an interest rate of i is:
For example: if I want to buy a bond that will pay $100,000 in 20 years with an interest rate of 8%, the cost would be:
If I decide to sell my bond after only 5 years, I can do the same computation using the new number of years and the current interest rate. If interest rates were now at 12%, my bond (which will now mature in 15 years) would be worth:
Yikes! I would lose over $3,000 by selling early! When interest rates rise, bonds lose some of their value. If interest rates decline, bonds gain value. Investor beware!!
9. You want to buy a bond that will be worth $100,000 in 30 years, with an annual interest rate of 7%. How much should you pay for this bond?
10. You decide to sell your bond after 5 years. Interest rates are now 9%. How much would you be able to sell your bond for? Will you lose money?