Simple and Compound Intersest
Today we will tackle problems where the type of interest will vary, it could either be simple or compound interest.
As a reminder the formulas for simple interest are:
- I = PRT (just the interest)
- A = PRT + P (the total amount)
The formula for compound interest is:
- A = P(1 + r/n)nt (the total amount)
- I = P(1 + r/n)nt - P (just the interest)
You will have to use each of these problems depending on what the question asks, here are a few examples:
Example 1 - Simple Interest, Just the Interest
Charlie steals $9,789 from Mav while he is sleeping. She invests it in Hollybank in Fightertown, USA. Hollybank earns 3% simple interest. If she leaves the money in the bank for 6 years, how much interest does she earn?
Notice this problem is asking us just for simple interest, thus we'll use the simple interest formula. The principal amount is $9,789, the interest is 3/100, and the time is 6 years.
The interest earned will be:
- I = $9,789 · (3/100) · 6 = $1,762.02
Example 2 - Simple Interest, Total Amount
Goose had invested $4,000 at a bank offering 6% simple interest for 5 years before he died. Carol, his grief stricken wife (thanks Mav), inherited the money after his death. How much did she inherit?
In this case, we'll use the second of the two simple interest formulas. The principal, P, is $4,000, the interest as a decimal is 0.06 (6/100), and the time is 5 years.
- A = $4,000 · 0.06 · 5 + $4,000 = $5,200
Example 3 - Compound Interest, Total Amount
Hangman invests $3,000 at a 2% compound interest rate. The interest is compounded monthly. He invests it for 3 years. If Hangman doesn't withdraw any money after 3 years, how much money does he have from the investment?
This question is asking for the total amount of compounded interest so we'll use the first of the two compound interest formulas. The principal is $3,000, the interest is 3/100 or 0.03, the amount of times the interest is compounded per year is 12 (monthly), and the time in years is 3.
Let's use the top equation for compound interest:
- A = $3,000(1 + 0.03/12)12 · 3 = $3,282.15
Example 4 - Compound Interest, Just the Interest
Slider and Viper are saving money for a restaurant near the runway. They invest $50,000 in the stock market. If the stock market earns 8% daily compounded interest, how much will they earn in interest after 5 years?
We'll use the 2nd of the compound interest formulas, noting that P = $50,000, r = 0.08, n = 365, and t = 5.
- I = $50,000(1 + 0.08/365)365 · 5 - $50,000 = $24,587.97