Question

1. Find the simple interest on a three-year investment with a principal of $10,000 at 4% annual interest note.

2. Now compute the compound interest on a three-year investment with a principal of 10,000 at 4% compound quarterly. Put your results in the form of a table.






3. Calculate the compound interest on a three-year investment with a principal of $10,000 at 4% compounded monthly. Write your conclusions without making a table.


4. If you had the same amount of money in an account collecting only simple interest, What would the yearly interest rate have to be to produce the same return as in number 3? Use the WP fourmula.

Answer 1

1. $1,200
2. $1,268.25
3. $1.272.72
4. 4.2424%

Explanation:

1. The interest is given by ...

I = Prt = ($10,000)(.04)(3) = $1,200

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2. The interest is given by ...

I = P((1 +r/n)^(nt) -1) = ($10,000)((1 +.04/4)^(4·3) -1) = $1,268.25

Here's a "table."

investment Simple Interest Compound Interest

$10,000 $1,200 $1,268.25

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3. Using the same compound interest formula with n=12, the interest is ...

I = P((1 +r/n)^(nt) -1) = ($10,000)((1 +.04/12)^(12·3) -1) = $1,272.72

More frequent compounding results in higher interest.

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4. We can use the formula of question 1:

I = Prt

1,272.72 = 10,000(r)(3)

r = 4.2424% . . . . . . divide by the coefficient of r

The simple interest rate would need to be 4.2424% to match interest compounded monthly for 3 years.