Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.

Correct Answer  $9454

Solution & Explanation

Solution

Given,

Principal (P) = $5800

Rate of Simple Interest (SI) = 7%

Time (t) = 9 years

Thus, Amount (A) = ?

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

Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $5800 × 7% × 9

= $5800 ×⁷/₁₀₀ × 9

= ^{5800 × 7 × 9}/₁₀₀

= ^{40600 × 9}/₁₀₀

= ³⁶⁵⁴⁰⁰/₁₀₀

= $3654

Thus, Simple Interest = $3654

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 = $5800 + $3654

= $9454

Thus, Amount to be paid = $9454 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 = $5800

Rate of Simple Interest (SI) or (R) = 7%

And, Time (t) = 9 years

Thus, Amount (A)

= $5800 + ($5800 × 7% × 9)

= $5800 + ($5800 ×⁷/₁₀₀ × 9)

= $5800 + (^{5800 × 7 × 9}/₁₀₀)

= $5800 + (^{40600 × 9}/₁₀₀)

= $5800 + (³⁶⁵⁴⁰⁰/₁₀₀)

= $5800 + $3654 = $9454

Thus, Amount (A) to be paid = $9454 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 7%

This, means, $7 per $100 per year

∵ For $100, the simple interest for 1 year = $7

∴ For $1, the simple interest for 1 year = ⁷/₁₀₀

∴ For $5800, the simple interest in 1 year

= ⁷/₁₀₀ × 5800

= ^{7 × 5800}/₁₀₀

= ⁴⁰⁶⁰⁰/₁₀₀ = $406

Thus, simple interest for 1 year = $406

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $406 × 9 = $3654

Thus, Simple Interest (SI) = $3654

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5800 + $3654

= $9454

Thus, Amount to be paid = $9454 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 $8804 to clear the loan, then find the time period of the loan.

(2) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.

(3) Joshua had to pay $5635 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.

(5) If Thomas paid $4408 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 9% simple interest?

(7) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.

(9) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.

(10) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.