Simple Interest
Math MCQs

Question :    Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 7 years.

Correct Answer  $9780

Solution & Explanation

Solution

Given,

Principal (P) = $6000

Rate of Simple Interest (SI) = 9%

Time (t) = 7 years

Thus, Amount (A) = ?

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

Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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) = $6000 × 9% × 7

= $6000 ×⁹/₁₀₀ × 7

= ^{6000 × 9 × 7}/₁₀₀

= ^{54000 × 7}/₁₀₀

= ³⁷⁸⁰⁰⁰/₁₀₀

= $3780

Thus, Simple Interest = $3780

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 = $6000 + $3780

= $9780

Thus, Amount to be paid = $9780 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 = $6000

Rate of Simple Interest (SI) or (R) = 9%

And, Time (t) = 7 years

Thus, Amount (A)

= $6000 + ($6000 × 9% × 7)

= $6000 + ($6000 ×⁹/₁₀₀ × 7)

= $6000 + (^{6000 × 9 × 7}/₁₀₀)

= $6000 + (^{54000 × 7}/₁₀₀)

= $6000 + (³⁷⁸⁰⁰⁰/₁₀₀)

= $6000 + $3780 = $9780

Thus, Amount (A) to be paid = $9780 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 9%

This, means, $9 per $100 per year

∵ For $100, the simple interest for 1 year = $9

∴ For $1, the simple interest for 1 year = ⁹/₁₀₀

∴ For $6000, the simple interest in 1 year

= ⁹/₁₀₀ × 6000

= ^{9 × 6000}/₁₀₀

= ⁵⁴⁰⁰⁰/₁₀₀ = $540

Thus, simple interest for 1 year = $540

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $540 × 7 = $3780

Thus, Simple Interest (SI) = $3780

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $6000 + $3780

= $9780

Thus, Amount to be paid = $9780 Answer

Similar Questions

(1) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.

(2) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 5% simple interest?

(3) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.

(4) How much loan did Edward borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9500 to clear it?

(5) Lisa had to pay $4414.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 3 years.

(7) Nancy had to pay $4772.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) If Donna paid $5820 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8940 to clear the loan, then find the time period of the loan.

(10) What amount will be due after 2 years if William borrowed a sum of $3250 at a 4% simple interest?