Simple Interest
Math MCQs

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

Correct Answer  $7450

Solution & Explanation

Solution

Given,

Principal (P) = $5000

Rate of Simple Interest (SI) = 7%

Time (t) = 7 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% × 7

= $5000 ×⁷/₁₀₀ × 7

= ^{5000 × 7 × 7}/₁₀₀

= ^{35000 × 7}/₁₀₀

= ²⁴⁵⁰⁰⁰/₁₀₀

= $2450

Thus, Simple Interest = $2450

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 + $2450

= $7450

Thus, Amount to be paid = $7450 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) = 7 years

Thus, Amount (A)

= $5000 + ($5000 × 7% × 7)

= $5000 + ($5000 ×⁷/₁₀₀ × 7)

= $5000 + (^{5000 × 7 × 7}/₁₀₀)

= $5000 + (^{35000 × 7}/₁₀₀)

= $5000 + (²⁴⁵⁰⁰⁰/₁₀₀)

= $5000 + $2450 = $7450

Thus, Amount (A) to be paid = $7450 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 7 years

= Simple interest for 1 year × 7

= $350 × 7 = $2450

Thus, Simple Interest (SI) = $2450

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5000 + $2450

= $7450

Thus, Amount to be paid = $7450 Answer

Similar Questions

(1) Michelle had to pay $5395.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(2) How much loan did James borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6000 to clear it?

(3) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 8% simple interest.

(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.

(5) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(6) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6664 to clear the loan, then find the time period of the loan.

(7) How much loan did Matthew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6820 to clear it?

(8) In how much time a principal of $3150 will amount to $3433.5 at a simple interest of 3% per annum?

(9) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 4 years.

(10) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.