# Math Questions Using Simple and Compound Interest

1) Bryan invests $500 in an account earning 4% interest that compounds annually. If he makes no additional deposits or withdraws, how much will be in the account:

a After 10 years?

b After 15 years?

c After 20 years?

d After 25 years?

e About how long would it take to double his $500 investment?

2) Lori buys a $1500 certificate of deposit (CD) that earns 6% interest that compounds monthly. How much will the CD be worth in:

a 5 years?

b 10 years?

c 18 months?

3) Lori gets an offer from another bank that is also paying 6% on CD's but is compounding interest daily. How much will the $1500 CD be worth in:

a 5 years?

b 10 years?

c 18 months?

4) You borrow $10,000 at 5% interest compounded weekly for tuition. While you do not have to make payments for the 5 years that you are in school, the interest is compounding every week. What is your loan balance after the 5 year grace period (if you've made no payments)?

5) Create an Excel spreadsheet comparing simple and interest compounded early for an investment of $1200 over 30 years with an APR of 8%.

a Use the directions fro class to create your spreadsheet showing both types of interest for all 30 years.

b Use the data from the spreadsheet to create a graphic (scatterplot) comparing the two types of interest. Write a paragraph making your comparisons and observations.

6) Perry has an opportunity to put $12,000 into an investment with an APR of 5.25%. How long will it take his investment to double? To quadruple?

7) The average population growth rate for whitetail deer is 0.35. Hunting laws are set to limit the time allowed for hunting deer with a goal of achieving about a 35% mortality rate on deer to keep the population in check. Years with a higher than 35% mortality will result in an overall decline in the deer population while years with a lower than 35% mortality rate will result in an increased population.

a If there were no hunting of whitetail deer allowed how long would it take the population of deer to double? To quadruple?

b if the growth rate exceeds the mortality rate, and the et effect were a 10% growth rate, how long would it take the population to double?

8) If the world's population growth rate continues to be 1.17%, how long before the population doubles?

9) Research the population growth rate for the U.S. and estimate how long it will take the population to double at that rate. Write a short paragraph explaining your process and results. Check your results for reasonableness.

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#### Solution Preview

1

Use A = P ( 1 + r/n) ^ (n * t) for the problem.

a

P = $500

r = 4% = 0.04

n = 1 (annual)

t = 10 years

Find A.

A = 500 ( 1 + 0.04/1) ^ (1 * 10) = $740.12

b

P = $500

r = 4% = 0.04

n = 1 (annual)

t = 15 years

Find A.

A = 500 ( 1 + 0.04/1) ^ (1 * 15) = $900.47

c

P = $500

r = 4% = 0.04

n = 1 (annual)

t = 20 years

Find A.

A = 500 ( 1 + 0.04/1) ^ (1 * 20) = $1,095.56

d

P = $500

r = 4% = 0.04

n = 1 (annual)

t = 25 years

Find A.

A = 500 ( 1 + 0.04/1) ^ (1 * 25) = $1,332.92

e

P = $500

A = 2 * $500 = $1,000

r = 4% = 0.04

n = 1 (annual)

Find t.

1,000 = 500 ( 1 + 0.04/1) ^ (1 * t)

1,000 = 500 (1.04)^t

(1.04)^t = 2

t = (log 2) / (log 1.04) = 17.7 years

2

Use A = P ( 1 + r/n) ^ (n * t) for the problem.

a

P = $1,500

r = 6% = 0.06

n = 12 (monthly)

t = 5 years

Find A.

A = 1,500 ( 1 + 0.06/12) ^ (12 * 5) = $2,023.28

b

P = $1,500

r = 6% = 0.06

n = 12 (monthly)

t = 10 years

Find A.

A = 1,500 ( 1 + 0.06/12) ^ (12 * 10) = $2,729.10

c

P = $1,500

r = 6% = 0.06

n = 12 (monthly)

t = 18 months = 1.5 years

Find A.

A = 1,500 ( 1 + 0.06/12) ^ (12 * ...

#### Solution Summary

Step-by-step solutions are provided. The Excel file contains the calculations, formulas, graphs and solutions for question #5.