Simple Interest
Math MCQs

Question :    Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 8 years.

Correct Answer  $10320

Solution & Explanation

Solution

Given,

Principal (P) = $6000

Rate of Simple Interest (SI) = 9%

Time (t) = 8 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% × 8

= $6000 ×⁹/₁₀₀ × 8

= ^{6000 × 9 × 8}/₁₀₀

= ^{54000 × 8}/₁₀₀

= ⁴³²⁰⁰⁰/₁₀₀

= $4320

Thus, Simple Interest = $4320

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 + $4320

= $10320

Thus, Amount to be paid = $10320 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) = 8 years

Thus, Amount (A)

= $6000 + ($6000 × 9% × 8)

= $6000 + ($6000 ×⁹/₁₀₀ × 8)

= $6000 + (^{6000 × 9 × 8}/₁₀₀)

= $6000 + (^{54000 × 8}/₁₀₀)

= $6000 + (⁴³²⁰⁰⁰/₁₀₀)

= $6000 + $4320 = $10320

Thus, Amount (A) to be paid = $10320 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 8 years

= Simple interest for 1 year × 8

= $540 × 8 = $4320

Thus, Simple Interest (SI) = $4320

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $6000 + $4320

= $10320

Thus, Amount to be paid = $10320 Answer

Similar Questions

(1) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.

(2) Joshua had to pay $5341 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.

(4) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 8% simple interest?

(5) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 4 years.

(7) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.

(8) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8580 to clear it?

(9) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 7 years.

(10) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.