PROBLEMS ON SIMPLE AND COMPOUND INTEREST

Problem 1 :

What is the profit of $650 in 6 years at the rate of profit 7% per annum?

Solution :

I = PNR/100

Here p = 650, N = 6 and R = 7%.

I = 650(6)(7)/100

I = 273

Problem 2 :

Find the compound principal and compound profit of $15000 in 3 years at a profit 6 percent per annum.

Solution :

Amount = P(1 + r)ⁿ

P = 15000, n = 3 and r = 6/100

Amount = 150000(1 + 6/100)³

= 15000(1.06)³

= 17865.24

Profit = 17865.24 - 15000

= $2865.24

Problem 3 :

If the simple profit of $300 in 4 years and a simple profit of $400 in 5 years together are $148. What is the percentage of profit?

Solution :

I₁ = P₁N₁R/100, I₂ = P₂N₂R/100

I₁ + I₂ = 148

P₁N₁R/100 + P₂N₂R/100 = 148

R[300 ⋅ 4 + 400 ⋅ 5] = 148

R[1200 + 2000] = 148

R = 148/3200

R = 0.04625

So, rate of interest is 4.6%.

Problem 4 :

If the difference of simple and compound profit of some principal in 2 years is $1 at the rate of profit 4%, what is the principal?

Solution :

Simple interest = PNR/100.

Compound interest = P[(1 + r)ⁿ - 1]

C.I - S.I = 1

P[(1 + r)ⁿ - 1] - PNR/100 = 1

P(1 + r)ⁿ - P - PNR/100 = 1

P[(1 + 0.4)² - P - P(2)(4)/100 = 1

1.0816P - P - 0.08P = 1

0.0016P = 1

P = 625

The principal is $625.

Problem 5 :

Some principal becomes $460 with simple profit in 3 years and $600 with the simple profit in 5 years. What is the rate of profit?

Solution :

Simple interest = PNR/100

Principal with profit in 3 years = 460

Principal with profit in 5 years = 600

Difference = 600 - 460

Principal with interest 2 years = 140

Principal with interest per year = 70

Interest for 3 years = 3(70) ==> 210

Principal with interest - interest for 3 years :

460 - 210 = 250

So, the required principal is $250.

I = PNR/100

210 = 250(3)(R)

R = 210/750

R = 0.28

So, the required rate of interest is 28%.

Problem 6 :

How much money will become $985 as a profit principal in 13 years at the rate of simple profit 5% per annum?

Solution :

P = ?, I = 985, N = 13 and R = 5

Principal + interest = 985

Interest = 985 - P

985 - P = P(13)(5)/100

98500 - 100P = 65P

98500 = 165P

P = 596

Problem 7 :

How much money will become $1248 as a profit in 12 years at the rate of 5% per annum?

Solution :

P + I = 1248, N = 12 and R = 5

Principal + interest = 1248

Interest = 1248 - P

1248 - P = P(12)(5)/100

124800 - 100P = 60P

124800 = 160P

P = 780

Problem 8 :

Find the difference of simple profit and compound profit of $800 in 3 years at the rate of 5%.

Solution :

Simple profit - Compound profit :

= P[(1 + r)ⁿ - 1] - PNR/100

= 800 {(1 + 0.05)³ - 1] - 3(0.05)}

= 800 {(1.05)³ - 1 - 0.15}

= 800 {1.157625 - 1.15}

= 800(0.007625)

= 6.1

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