Simple Interest
Math MCQs

Question :    Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 3 years.

Correct Answer  $4312

Solution & Explanation

Solution

Given,

Principal (P) = $3850

Rate of Simple Interest (SI) = 4%

Time (t) = 3 years

Thus, Amount (A) = ?

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

Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $3850 × 4% × 3

= $3850 ×⁴/₁₀₀ × 3

= ^{3850 × 4 × 3}/₁₀₀

= ^{15400 × 3}/₁₀₀

= ⁴⁶²⁰⁰/₁₀₀

= $462

Thus, Simple Interest = $462

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 = $3850 + $462

= $4312

Thus, Amount to be paid = $4312 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 = $3850

Rate of Simple Interest (SI) or (R) = 4%

And, Time (t) = 3 years

Thus, Amount (A)

= $3850 + ($3850 × 4% × 3)

= $3850 + ($3850 ×⁴/₁₀₀ × 3)

= $3850 + (^{3850 × 4 × 3}/₁₀₀)

= $3850 + (^{15400 × 3}/₁₀₀)

= $3850 + (⁴⁶²⁰⁰/₁₀₀)

= $3850 + $462 = $4312

Thus, Amount (A) to be paid = $4312 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 4%

This, means, $4 per $100 per year

∵ For $100, the simple interest for 1 year = $4

∴ For $1, the simple interest for 1 year = ⁴/₁₀₀

∴ For $3850, the simple interest in 1 year

= ⁴/₁₀₀ × 3850

= ^{4 × 3850}/₁₀₀

= ¹⁵⁴⁰⁰/₁₀₀ = $154

Thus, simple interest for 1 year = $154

Therefore, simple interest for 3 years

= Simple interest for 1 year × 3

= $154 × 3 = $462

Thus, Simple Interest (SI) = $462

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3850 + $462

= $4312

Thus, Amount to be paid = $4312 Answer

Similar Questions

(1) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.

(2) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.

(3) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.

(4) How much loan did Mary borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6312.5 to clear it?

(5) How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?

(6) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.

(7) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.

(8) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 10% simple interest.

(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 7 years.