Simple Interest
Math MCQs

Question :    Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.

Correct Answer  $6786

Solution & Explanation

Solution

Given,

Principal (P) = $5850

Rate of Simple Interest (SI) = 2%

Time (t) = 8 years

Thus, Amount (A) = ?

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

Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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) = $5850 × 2% × 8

= $5850 ײ/₁₀₀ × 8

= ^{5850 × 2 × 8}/₁₀₀

= ^{11700 × 8}/₁₀₀

= ⁹³⁶⁰⁰/₁₀₀

= $936

Thus, Simple Interest = $936

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 = $5850 + $936

= $6786

Thus, Amount to be paid = $6786 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 = $5850

Rate of Simple Interest (SI) or (R) = 2%

And, Time (t) = 8 years

Thus, Amount (A)

= $5850 + ($5850 × 2% × 8)

= $5850 + ($5850 ײ/₁₀₀ × 8)

= $5850 + (^{5850 × 2 × 8}/₁₀₀)

= $5850 + (^{11700 × 8}/₁₀₀)

= $5850 + (⁹³⁶⁰⁰/₁₀₀)

= $5850 + $936 = $6786

Thus, Amount (A) to be paid = $6786 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 2%

This, means, $2 per $100 per year

∵ For $100, the simple interest for 1 year = $2

∴ For $1, the simple interest for 1 year = ²/₁₀₀

∴ For $5850, the simple interest in 1 year

= ²/₁₀₀ × 5850

= ^{2 × 5850}/₁₀₀

= ¹¹⁷⁰⁰/₁₀₀ = $117

Thus, simple interest for 1 year = $117

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $117 × 8 = $936

Thus, Simple Interest (SI) = $936

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5850 + $936

= $6786

Thus, Amount to be paid = $6786 Answer

Similar Questions

(1) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 3 years.

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

(4) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 3% simple interest?

(5) What amount does William have to pay after 5 years if he takes a loan of $3500 at 6% simple interest?

(6) If Susan paid $4380 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.

(8) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 4% simple interest?

(9) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 8 years.