Simple Interest
Math MCQs

Question :    Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 7 years.

Correct Answer  $8892

Solution & Explanation

Solution

Given,

Principal (P) = $5700

Rate of Simple Interest (SI) = 8%

Time (t) = 7 years

Thus, Amount (A) = ?

The Rate of Interest is always calculated per annum, i.e. per year.

Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% per annum.

Method (1) Using Formula

Calculation of Simple Interest

Formula to Calculate Simple Interest

Simple Interest (SI) = Principal × Rate × Time

Thus, Simple Interest (SI) = $5700 × 8% × 7

= $5700 ×⁸/₁₀₀ × 7

= ^{5700 × 8 × 7}/₁₀₀

= ^{45600 × 7}/₁₀₀

= ³¹⁹²⁰⁰/₁₀₀

= $3192

Thus, Simple Interest = $3192

Calculation of Amount

The total money paid to the lender by a borrower is called the Amount.

In other words, sum of priciple and interest is called the Amount.

Formula to Calculate the Amount

Amount = Principal + Interest

Thus, Amount = $5700 + $3192

= $8892

Thus, Amount to be paid = $8892 Answer

Method (2)

Calculation of Amount when Principal, Rate of Simple Interest and Time are given

Calculation of Amount directly using Principal, SI, and Time

Formula to calculate the Amount

Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)

⇒ A = P + PRT

Here in the question, P = $5700

Rate of Simple Interest (SI) or (R) = 8%

And, Time (t) = 7 years

Thus, Amount (A)

= $5700 + ($5700 × 8% × 7)

= $5700 + ($5700 ×⁸/₁₀₀ × 7)

= $5700 + (^{5700 × 8 × 7}/₁₀₀)

= $5700 + (^{45600 × 7}/₁₀₀)

= $5700 + (³¹⁹²⁰⁰/₁₀₀)

= $5700 + $3192 = $8892

Thus, Amount (A) to be paid = $8892 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 8%

This, means, $8 per $100 per year

∵ For $100, the simple interest for 1 year = $8

∴ For $1, the simple interest for 1 year = ⁸/₁₀₀

∴ For $5700, the simple interest in 1 year

= ⁸/₁₀₀ × 5700

= ^{8 × 5700}/₁₀₀

= ⁴⁵⁶⁰⁰/₁₀₀ = $456

Thus, simple interest for 1 year = $456

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $456 × 7 = $3192

Thus, Simple Interest (SI) = $3192

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5700 + $3192

= $8892

Thus, Amount to be paid = $8892 Answer

Similar Questions

(1) William had to pay $3710 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 3 years.

(4) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.

(5) If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?

(8) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.

(9) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?

(10) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.