Interest Problems

The interest earned equals the interest rate times the amount of money (or principal) invested times the time (as part of one year). We let i = interest, p = principal, r = interest rate, and t = time as part of 1 year, then i = prt.

EXAMPLE 1: Part of Dollar Bill's $4000 is invested in a bank at 6% and the other part in 8% interest - yielding bonds. His annual income from the two sources is $260. How much has Bill in the bank?

P

´

r

´

t

=

i

in bank

x

 

.06

 

1

  .06x

in bond

4000-x

   

.08

   

1

    .08(4000-x)

total

4000

      260


M100
D2

.06x + .08(4000 - x) = 260
6x + 8(4000 - x) = 26000
3x + 4(4000 - x) = 13000
3x + 16,000 - 4x = 13000
-x = -3000
x = 3000

Bill has $3000 in the bank

EXAMPLE 2: Smart Sam invests $1000 more at 9% than in a Safer investment at 6%. He earns the same as if the entire amount were invested at 8 1/2%. How much has Sam invested at 6%?

P

´

r

´

t

=

i

x

   

6%

   

1

    .06(x)

x+1000

   

9%

   

1 

    .09(x+1000)

2x+1000

   

8.5%

   

1

    .085(2x+1000)


M1000 .06x + .09(x + 1000) = .085(2x+1000)
60x + 90(x + 1000) = 85(2x + 1000)
60x + 90x + 99000 = 170x + 85000
5000 = 20x
250 = x
Therefore, Sam invested 250 at 6%.

PROBLEMS:

1. How much interest is earned in one year on a principal of $560 if the annual interest rate is 6%?

2. What is the annual interest rate of $88 interest is paid in a year on a principal of $2200?

3. How much money must be invested for a year at 7% in order to earn $249.50 interest?

4. A sum of $2500 is left for two years in a bank that pays an annual interest rate of 5%. How much interest is earned?

5. If you have twice as much invested at 7% as at 5% and if your annual interest income from these two investments is $950, how much have you invested at each rate?

6. A Company invests $12000 at 5% and $18,000 at 6%. At what rate should it invest its remaining $5000 in order to receive a combined interest of $2030?

7. A man has a total of $15,000 in 3 investments. One of the investments is bonds that pay 6 percent annual interest, another is a savings account that pays 5% annual interest, and the third is a business. Two years ago the business lost 3% and his net income from the 3 investments was $550. Last year the business earned 9 percent and his net income was $910. How much does he have in each investment?

8. Part of 25,000 is invested at 5% another part is invested in 6%; and a third part is invested at 8%. The total yearly income from the three investments is $1600. Furthermore, the income form the 8 percent investment yields the same amount as the sum of the incomes from the other two investments. How much was invested at each rate?

ANSWERS:

1. $33.60

2. 4%

3. $35.65

4. $256.25

5. 5,000 at 5% and $10,000 at 7%

6. 7%

7. $4,000 in bonds, $8,000 in savings and $3,000 in the business

8. $10,000 at 5%, $5,000 at 6% and 10,000 at 8%