MBA 13.1 HW
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Apr 3, 2024
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Uploaded by DoctorRaccoon2667
Math with Business Applications
13.1 Homework Assignment
Spring 2023
Name: Directions
: Complete these problems using formulas or Excel. All problems should show your calculations (or a screenshot of your work in Excel). The answers are at the bottom of the page for you to reference. Once you are finished, please upload the document to Blackboard. 1.
Suppose Troy received $5,000 from the COVID stimulus. He plans to place the money in an interest-
bearing account that earns 8% interest per year. a.
If the account is a simple interest account, how much interest will he earn after 5 years? 5000*.08*5 = $2,000
b.
What is the maturity value of the account? MV: 5000+2000 = $7,000
c.
If the account is a compound interest account where interest is compounded annually, what is the future value of the account after 5 years? Use formulas or Excel. 5000(1+.08/1)^1*5 = $7,346.64
d.
How much more interest was earned in the compound interest account? 7346.64-7000 = $346.64
2.
Kayley prefers accounts that ‘compound’ more frequently. Suppose she works with the same $5,000 at 8% compound interest.
a.
How much money will her account have in 5 years if interest is compounded semiannually? Use formulas or Excel.
5000(1+.08/2)^2*5 = $7,401.22
b.
How much money will her account have in 5 years if interest is compounded quarterly? Use formulas or Excel.
5000(1+.08/4)^4*5 = $7,429.74
c.
How much money will her account have in 5 years if interest is compounded monthly? Use formulas or Excel.
5000(1+.08/12)^12*5 = $7,449.23
d.
Why does compounding more often increase the future value of the account? 3.
Leori is deciding between a simple interest account and a compound interest account. Suppose she was gifted $15,000 to put toward the future college costs for her kids. The simple interest account earns 8% annually while the compound interest account earns 6% compounded monthly. a.
Which account is the better choice if she were to leave the money in the account for 5 years? Explain your thinking and be sure to show your calculations. 15000*.08*5 = $6,000
15000(1+.06/12)^12*5 = $20,232.75
b.
Which account is the better choice if she were to leave the money in the account for 10 years? Explain your thinking and be sure to show your calculations.
c.
Which account is the better choice if she were to leave the money in the account for 15 years? Explain your thinking and be sure to show your calculations.
d.
How is simple interest different than compound interest? In other words, how did compound interest catch up and totally crush the simple interest account after 15 years?
4.
Effective interest rates are a way to describe compound interest rates on an annual basis instead of by quarter, month, etc. It is the equivalent simple interest rate for 1 year. a.
From problem 2, Kayley’s $5,000 grew to $7,429.74 after 5 years in the compound interest account where compounding happened each quarter. How much interest did she earn after the first year?
b.
Now, divide the interest for one year by the principal. What is the effective interest rate? (Write several numbers after the decimal point for accuracy). c.
Show that you can multiply $5,000 by this annual
interest rate for 5 years and get $7,429.74. Use formulas or Excel where n=1 and t=5.
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d.
From problem 3, Leori’s $15,000 grew to $36,811.40 over 15 years when interest was 6% compounded monthly. Find the effective (annual) rate of interest. Then, show that you can multiply
by that annual rate (15 times!) to get $36,811.40 (or very close). HW Answers:
1a: $2,000
1b: $7,000
1c: $7,346.64
1d: $346.64
2a: $7,401.22
2b: $7,429.74
2c: $7,449.23
2d: As the account value increases, so too does the interest earned every time it compounds. 3a: Simple interest account is greater by $767.25.
3b: Compound interest account is greater by $290.95
3c: Compound interest account by $3,811.40
3d: Simple interest adds the same amount each year. Compound interest earns interest on interest!
4a: $412.16
4b: 0.08243216 or 8.243216%
4c: $5,000(1+0.08243216)^5 4d: 0.061677811864 or 6.1677811864%
$15,000(1+0.061677811864)^15
Note: It would be okay to express this rate as 6.17%. In your calculations though – don’t round – just leave that very long decimal in your calculator. (If you find a mistake in the answers, because I’m human and it’s possible, bonus points!)