Simple Interest
Math MCQs

Question :    Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 4 years.

Correct Answer  $3720

Solution & Explanation

Solution

Given,

Principal (P) = $3100

Rate of Simple Interest (SI) = 5%

Time (t) = 4 years

Thus, Amount (A) = ?

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

Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $3100 × 5% × 4

= $3100 ×⁵/₁₀₀ × 4

= ^{3100 × 5 × 4}/₁₀₀

= ^{15500 × 4}/₁₀₀

= ⁶²⁰⁰⁰/₁₀₀

= $620

Thus, Simple Interest = $620

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 = $3100 + $620

= $3720

Thus, Amount to be paid = $3720 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 = $3100

Rate of Simple Interest (SI) or (R) = 5%

And, Time (t) = 4 years

Thus, Amount (A)

= $3100 + ($3100 × 5% × 4)

= $3100 + ($3100 ×⁵/₁₀₀ × 4)

= $3100 + (^{3100 × 5 × 4}/₁₀₀)

= $3100 + (^{15500 × 4}/₁₀₀)

= $3100 + (⁶²⁰⁰⁰/₁₀₀)

= $3100 + $620 = $3720

Thus, Amount (A) to be paid = $3720 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 5%

This, means, $5 per $100 per year

∵ For $100, the simple interest for 1 year = $5

∴ For $1, the simple interest for 1 year = ⁵/₁₀₀

∴ For $3100, the simple interest in 1 year

= ⁵/₁₀₀ × 3100

= ^{5 × 3100}/₁₀₀

= ¹⁵⁵⁰⁰/₁₀₀ = $155

Thus, simple interest for 1 year = $155

Therefore, simple interest for 4 years

= Simple interest for 1 year × 4

= $155 × 4 = $620

Thus, Simple Interest (SI) = $620

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3100 + $620

= $3720

Thus, Amount to be paid = $3720 Answer

Similar Questions

(1) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.

(2) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 9% simple interest?

(3) What amount will be due after 2 years if John borrowed a sum of $3100 at a 8% simple interest?

(4) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?

(5) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 8% simple interest.

(6) How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?

(7) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.

(8) Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.

(10) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.