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I need help on Simple Interest.

I was absent on the day my class learned how to do it. I kind of got an understanding of how to do it from the math book, but I still got my answers wrong. I need to understand how to put the problem together. Please help me with these. Thanks!

 

1. How much simple interest is earned on a deposit of $500 at an annual rate of 6% after 3 months?

 

2. How much money is in your account after 5 years if you deposited $900 earning simple interest at 4.5%?

 

3. Mrs. Jones deposited $1000 in a savigns account earning simple interest. After 2 years, Mrs. Jones had    earned $210 interest. What was the interest rate?

 

4. Danny  buys a house that costs $100,000. The bank gave him a 30-year loan with an interest rate of 6.5%. Hoow much will he end up spending on the house total, including interest?

 

5. The bank gave Carrie a $6000 loan to buy a car. She made payments of $140 every month for 4 years. What was the interest rate?

 

Comments

Let's get you started, then maybe you can finish on your own...  Basic formula I bet all the rest got in your misses class(es):  I=PRT.  That says simple Interest (in dollars, not %) = the Principal (original amount paid or borrowed, like a down payment) times the Rate (that's the interest rate % for 1 year, expressed as a decimal, so 5% = 0.05), times Time (in years; convert months into the decimal or fraction part of 1 year).  So for #1 in your problem: I=PRT;  I=($500)*(0.06)*(0.25) (6% = 0.06, and 3 months = 1/4 of a year)

Multiply all 3:  I=$7.50   Now you try the others, let meknow how you are doing.  You can rearrange that basic formula to solve for any of the missing parts, such as:  to get time (T), divide I by P*R, so you have T = I / PR.

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2 Answers

Courtney,

For 1 & 3, Simple Interest equals Principal times Interest rate times time (I = Prt).  One of the things to remember (and often not discussed in textbooks) is that interest rates are percentages per unit time, e.g. 10% interest per year; 1.5% interest per month.  So if you have $100 at 10% interest (.1) per year, in the bank for a year, the simple interest is $10 [$10 = ($100) * (.1/yr.) * (1 yr.)].  But if you keep the $100 in the bank for only 6 months, the simple interest is only $5 [$5 = ($100) * (.1/yr.) * (1/2 yr.)]  For #1, you have to adjust rate to account for the time the money was in the account.  For #3, you are given the interest, principal, and time, and asked to compute the rate, so r = I/Pt

For #2, In simple interest, the formula only accounts for the interest owed, and so the principal remains outstanding.  So in the $100 @ 10% for 1 year example, there would be $110 in the bank account $100 in principal and $10 in interest, i.e. the amount in the account is P + I where I = Prt.

For 4 & 5, your text should have examples of how to calculate these situations.  The issue is how to address the partial payments of principal over time.  For example, in #5, One way to calculate this using "simple interest" is to note that Carrie has paid 4 * 12 * $140 = $6720.  She has to pay the $6000 in principal, and so pays $720 in interest.  Using r = I/Pt, will give a simple interest rate. 

There are more complicated methods to address the fact that of her $140/mo. payment is only $15 in interest and $125 principal, and so the amount of principal owed should be reduced over time, but usually this is addressed as part of compound interest.  If there are models in your text addressing this situation, you should use those instead of the one above, especially for #4.

If you have an example from your text, I would be happy to walk you through it, and I hope this helps.  John

What you are missing is a simple formula:  I=PRT.  Means Interest (in dollars, not %) = Principal (downpayment or original savings) X Rate (percentage rate as a decimal:  5% = 0.05) X Time (in years - convert months into decimal part of 1 year).  You can also change that formula around.  For example, to find Time, divide Interest by Principal X Rate (T = I / PR).

To get you started, here's #1 in your problem list:  I = PRT.  I = $500 * 0.06 * 0.25 (0.06 = 6% and 0.25 = 3 months of 1 year).  Multiply it out:  I = $7.50.  Now you can do the rest!

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