1) Suppose you put $1,000 in a savings account that earns 3% interest per year. How much interest will you earn in one year?

2.     you put the same $1,000 in a savings account earning 5% interest per year. How much interest would you earn in three years?

3.     If you invest $500 in a simple interest account earning 6% simple interest per month, what will be the total value of the account after 10 months?

4.     If you put $800 in a simple interest account earning 5.2% interest per month, how much interest will you have earned after two years?

 

5.     How much would you have to invest in an account earning 5% simple interest every year to earn $50 after two years?

6.     What annual interest rate would you have to get to earn $85 interest on a $450 investment after five years?

Analysis Questions

7.     Redo Example 2 but assume that the interest is paid every month instead of every year. Discuss the difference between monthly versus annual interest.

8.     Suppose you invest $1,200 in an account that earns 4% simple interest every year. What interest rate would you have to get to make the same amount of interest if the simple interest were calculated every month instead of every year?

9.     If you invest $1,500 in an account that earns 5% simple interest per year, how long would you have to leave the money in your account to double your investment? (Remember that the I in the formula is just the interest earned.)

10.  If you invest $5,000 in a simple interest account at 4.6% for two years, what interest rate would you have to get to earn the same amount of interest in one year?

11.  If you have $500 to invest and assuming that you're paid simple interest, would you be better off putting it in an account that earns 5% per year for one year or an account that earns 1% per month for six months?

 

1) $30

2) $150

3) $800

4) $998.40

5) $45.45

6) 3.78% per year

7) The interest earned is $1800 if the interest is paid every month. It is higher than the interest earned if paid every year.

8) 0.33% per month

9) 20 years

10) 9.2% per year

11) You better put off your investment in the account that pays 1% per month for six years because if offers higher interest than the account that pays 5% per year.

Step-by-step explanation

The general formula of a simple interest is:

 

F = P[1 + (r)(t)] --> Formula 1

 

and

 

I = Prt --> Formula 2

 

where:

 

F = future value

P = present value

r = rate of simple interest

t = time

 

1) Suppose you put $1,000 in a savings account that earns 3% interest per year. How much interest will you earn in one year?

 

P = $1,000

r = 3% = 0.03 per year

t = 1 year

I = ?

 

Use Formula 2:

 

I = Prt

I = ($1,000)(0.03)(1)

I = $30

 

2) You put the same $1,000 in a savings account earning 5% interest per year. How much interest would you earn in three years?

 

P = $1,000

r = 5% = 0.05 per year

t = 3 years

I = ?

 

Use Formula 2:

 

I = Prt

I = ($1,000)(0.05)(3)

I = $150

 

3) If you invest $500 in a simple interest account earning 6% simple interest per month, what will be the total value of the account after 10 months?

 

P = $500

r = 6% = 0.06 per month

F = ?

t = 10 months

 

Use Formula 1:

 

F = P[1 + (r)(t)]

F = ($500)[1 + (0.06)(10)]

F = $800

 

4) If you put $800 in a simple interest account earning 5.2% interest per month, how much interest will you have earned after two years?

 

P = $800

r = 5.2% = 0.052 per month

t = 2 years = 2 years * 12 months per year = 24 months

I = ?

 

Use Formula 2:

 

I = Prt

I = ($800)(0.052)(24)

I = $998.40

 

5) How much would you have to invest in an account earning 5% simple interest every year to earn $50 after two years?

 

P = ?

r = 5% = 0.05 per year

F = $50

t = 2 years

 

Use Formula 1:

 

F = P[1 + (r)(t)]

50 = P[1 + (0.05)(2)]

50 = P(1.1)

P = ⁵⁰/_1.1

P = $45.45

 

6) What annual interest rate would you have to get to earn $85 interest on a $450 investment after five years?

 

r = ?

I = $85

P = $450

t = 5 years

 

Use Formula 2:

 

I = Prt

85 = (450)(r)(5)

85 = 2250r

r = ⁸⁵/₂₂₅₀

r = 0.0378 = 3.78% per year

 

7) Redo Example 2 but assume that the interest is paid every month instead of every year. Discuss the difference between monthly versus annual interest.

 

I assume you mean by "Example 2" is Problem 2: You put the same $1,000 in a savings account earning 5% interest per year. How much interest would you earn in three years?

 

P = $1,000

r = 5% = 0.05 per month

t = 3 years = 3 years * 12 months per year = 36 months

I = ?

 

Use Formula 2:

 

I = Prt

I = (1000)(0.05)(36)

I = $1800

 

The interest earned is $1800 if the interest is paid every month. It is higher than the interest earned if paid every year.

 

8) Suppose you invest $1,200 in an account that earns 4% simple interest every year. What interest rate would you have to get to make the same amount of interest if the simple interest were calculated every month instead of every year?

 

Case 1: interest is calculated every year

 

P = $1,200

r = 4% = 0.04

t = 1 year

 

The interest earned after a year is:

 

Use Formula 2:

 

I = Prt

I = (1200)(0.04)(1)

I = $48

 

Case 2: interest is calculated every month

 

P = $1,200

r = ?

t = 12 months (there are 12 months in a year)

I = $48 (same interest with Case 1)

 

Use Formula 2:

 

I = Prt

48 = (1200)(r)(12)

48 = 14400r

r = ⁴⁸/₁₄₄₀₀

r = 0.0033 = 0.33% per month

 

9) If you invest $1,500 in an account that earns 5% simple interest per year, how long would you have to leave the money in your account to double your investment?

 

P = $1,500

r = 5% = 0.05 per year

t = ?

F = double of the amount P = 2 * $1,500 = $3,000

 

Use Formula 1:

 

F = P[1 + (r)(t)]

3000 = (1500)(1 + (0.05)(t)]

3000 = 1500(1 + 0.05t)

3000 = 1500 + 75t

75t = 3000 - 1500

75t = 1500

t = ¹⁵⁰⁰/₇₅

t = 20 years

 

10) If you invest $5,000 in a simple interest account at 4.6% for two years, what interest rate would you have to get to earn the same amount of interest in one year?

 

Case 1: investment for 2 years

 

P = $5,000

r = 4.6% = 0.046 per year

t = 2 years

 

The interest earned is:

 

Use Formula 2:

 

I = Prt

I = (5000)(0.046)(2)

I = $460

 

Case 2: investment for 1 year

 

P = $5,000

r = ?

t = 1 year

I = $460 (Same interest in Case 1)

 

Use Formula 2:

 

I = Prt

460 = (5000)(r)(1)

460 = 5000r

r = ⁴⁶⁰/₅₀₀₀

r = 0.092 = 9.2% per year

 

11) If you have $500 to invest and assuming that you're paid simple interest, would you be better off putting it in an account that earns 5% per year for one year or an account that earns 1% per month for six months?

 

Case 1: rate is 5% per year

P = $500

r = 5% = 0.05 per year

t = 1 year

I = ?

 

The interest earned for Case 1 is:

 

Use Formula 2:

 

I = Prt

I = (500)(0.05)(1)

I = $25

 

Case 2: rate is 1% per month

P = $500

r = 1% = 0.01 per month

t = 6 months

I = ?

 

The interest earned for Case 2 is:

 

Use Formula 2:

 

I = Prt

I = (500)(0.01)(6)

I = $30

 

You better put off your investment in the account that pays 1% per month for six years because if offers higher interest than the account that pays 5% per year.