Simple Interest
Math MCQs

Question :    Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 7 years.

Correct Answer  $8307

Solution & Explanation

Solution

Given,

Principal (P) = $5850

Rate of Simple Interest (SI) = 6%

Time (t) = 7 years

Thus, Amount (A) = ?

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

Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $5850 × 6% × 7

= $5850 ×⁶/₁₀₀ × 7

= ^{5850 × 6 × 7}/₁₀₀

= ^{35100 × 7}/₁₀₀

= ²⁴⁵⁷⁰⁰/₁₀₀

= $2457

Thus, Simple Interest = $2457

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 = $5850 + $2457

= $8307

Thus, Amount to be paid = $8307 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 = $5850

Rate of Simple Interest (SI) or (R) = 6%

And, Time (t) = 7 years

Thus, Amount (A)

= $5850 + ($5850 × 6% × 7)

= $5850 + ($5850 ×⁶/₁₀₀ × 7)

= $5850 + (^{5850 × 6 × 7}/₁₀₀)

= $5850 + (^{35100 × 7}/₁₀₀)

= $5850 + (²⁴⁵⁷⁰⁰/₁₀₀)

= $5850 + $2457 = $8307

Thus, Amount (A) to be paid = $8307 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 6%

This, means, $6 per $100 per year

∵ For $100, the simple interest for 1 year = $6

∴ For $1, the simple interest for 1 year = ⁶/₁₀₀

∴ For $5850, the simple interest in 1 year

= ⁶/₁₀₀ × 5850

= ^{6 × 5850}/₁₀₀

= ³⁵¹⁰⁰/₁₀₀ = $351

Thus, simple interest for 1 year = $351

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $351 × 7 = $2457

Thus, Simple Interest (SI) = $2457

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5850 + $2457

= $8307

Thus, Amount to be paid = $8307 Answer

Similar Questions

(1) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?

(2) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7152 to clear the loan, then find the time period of the loan.

(3) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.

(4) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 10% simple interest?

(6) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6392 to clear the loan, then find the time period of the loan.

(7) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(8) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 8 years.

(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 3 years.