Simple Interest
Math MCQs

Question :    Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 8 years.

Correct Answer  $9116

Solution & Explanation

Solution

Given,

Principal (P) = $5300

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) = $5300 × 9% × 8

= $5300 ×⁹/₁₀₀ × 8

= ^{5300 × 9 × 8}/₁₀₀

= ^{47700 × 8}/₁₀₀

= ³⁸¹⁶⁰⁰/₁₀₀

= $3816

Thus, Simple Interest = $3816

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 = $5300 + $3816

= $9116

Thus, Amount to be paid = $9116 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 = $5300

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

And, Time (t) = 8 years

Thus, Amount (A)

= $5300 + ($5300 × 9% × 8)

= $5300 + ($5300 ×⁹/₁₀₀ × 8)

= $5300 + (^{5300 × 9 × 8}/₁₀₀)

= $5300 + (^{47700 × 8}/₁₀₀)

= $5300 + (³⁸¹⁶⁰⁰/₁₀₀)

= $5300 + $3816 = $9116

Thus, Amount (A) to be paid = $9116 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 $5300, the simple interest in 1 year

= ⁹/₁₀₀ × 5300

= ^{9 × 5300}/₁₀₀

= ⁴⁷⁷⁰⁰/₁₀₀ = $477

Thus, simple interest for 1 year = $477

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $477 × 8 = $3816

Thus, Simple Interest (SI) = $3816

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5300 + $3816

= $9116

Thus, Amount to be paid = $9116 Answer

Similar Questions

(1) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.

(2) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.

(3) How much loan did David borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5940 to clear it?

(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 8 years.

(5) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 6% simple interest?

(6) Jessica had to pay $4087.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(7) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 6% simple interest?

(8) If Robert paid $3596 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 8 years.

(10) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.