Simple Interest
Math MCQs

Question :    Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 8 years.

Correct Answer  $7800

Solution & Explanation

Solution

Given,

Principal (P) = $5000

Rate of Simple Interest (SI) = 7%

Time (t) = 8 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) = $5000 × 7% × 8

= $5000 ×⁷/₁₀₀ × 8

= ^{5000 × 7 × 8}/₁₀₀

= ^{35000 × 8}/₁₀₀

= ²⁸⁰⁰⁰⁰/₁₀₀

= $2800

Thus, Simple Interest = $2800

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 = $5000 + $2800

= $7800

Thus, Amount to be paid = $7800 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 = $5000

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

And, Time (t) = 8 years

Thus, Amount (A)

= $5000 + ($5000 × 7% × 8)

= $5000 + ($5000 ×⁷/₁₀₀ × 8)

= $5000 + (^{5000 × 7 × 8}/₁₀₀)

= $5000 + (^{35000 × 8}/₁₀₀)

= $5000 + (²⁸⁰⁰⁰⁰/₁₀₀)

= $5000 + $2800 = $7800

Thus, Amount (A) to be paid = $7800 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 $5000, the simple interest in 1 year

= ⁷/₁₀₀ × 5000

= ^{7 × 5000}/₁₀₀

= ³⁵⁰⁰⁰/₁₀₀ = $350

Thus, simple interest for 1 year = $350

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $350 × 8 = $2800

Thus, Simple Interest (SI) = $2800

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5000 + $2800

= $7800

Thus, Amount to be paid = $7800 Answer

Similar Questions

(1) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7897 to clear the loan, then find the time period of the loan.

(2) How much loan did David borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6210 to clear it?

(3) If James borrowed $3000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(4) Steven had to pay $4876 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.

(6) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) How much loan did James borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5750 to clear it?

(8) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 8 years.

(10) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.