Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.

Correct Answer  $9945

Solution & Explanation

Solution

Given,

Principal (P) = $5850

Rate of Simple Interest (SI) = 7%

Time (t) = 10 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) = $5850 × 7% × 10

= $5850 ×⁷/₁₀₀ × 10

= ^{5850 × 7 × 10}/₁₀₀

= ^{40950 × 10}/₁₀₀

= ⁴⁰⁹⁵⁰⁰/₁₀₀

= $4095

Thus, Simple Interest = $4095

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 + $4095

= $9945

Thus, Amount to be paid = $9945 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) = 7%

And, Time (t) = 10 years

Thus, Amount (A)

= $5850 + ($5850 × 7% × 10)

= $5850 + ($5850 ×⁷/₁₀₀ × 10)

= $5850 + (^{5850 × 7 × 10}/₁₀₀)

= $5850 + (^{40950 × 10}/₁₀₀)

= $5850 + (⁴⁰⁹⁵⁰⁰/₁₀₀)

= $5850 + $4095 = $9945

Thus, Amount (A) to be paid = $9945 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 $5850, the simple interest in 1 year

= ⁷/₁₀₀ × 5850

= ^{7 × 5850}/₁₀₀

= ⁴⁰⁹⁵⁰/₁₀₀ = $409.5

Thus, simple interest for 1 year = $409.5

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $409.5 × 10 = $4095

Thus, Simple Interest (SI) = $4095

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5850 + $4095

= $9945

Thus, Amount to be paid = $9945 Answer

Similar Questions

(1) How much loan did Mark borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7040 to clear it?

(2) What amount does David have to pay after 6 years if he takes a loan of $3400 at 3% simple interest?

(3) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 4% simple interest?

(4) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 3 years.

(5) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 3 years.

(7) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 4 years.

(8) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12127 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.

(10) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.