Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.

Correct Answer  $10530

Solution & Explanation

Solution

Given,

Principal (P) = $5850

Rate of Simple Interest (SI) = 8%

Time (t) = 10 years

Thus, Amount (A) = ?

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

Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 10

= $5850 ×⁸/₁₀₀ × 10

= ^{5850 × 8 × 10}/₁₀₀

= ^{46800 × 10}/₁₀₀

= ⁴⁶⁸⁰⁰⁰/₁₀₀

= $4680

Thus, Simple Interest = $4680

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 + $4680

= $10530

Thus, Amount to be paid = $10530 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) = 8%

And, Time (t) = 10 years

Thus, Amount (A)

= $5850 + ($5850 × 8% × 10)

= $5850 + ($5850 ×⁸/₁₀₀ × 10)

= $5850 + (^{5850 × 8 × 10}/₁₀₀)

= $5850 + (^{46800 × 10}/₁₀₀)

= $5850 + (⁴⁶⁸⁰⁰⁰/₁₀₀)

= $5850 + $4680 = $10530

Thus, Amount (A) to be paid = $10530 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 8%

This, means, $8 per $100 per year

∵ For $100, the simple interest for 1 year = $8

∴ For $1, the simple interest for 1 year = ⁸/₁₀₀

∴ For $5850, the simple interest in 1 year

= ⁸/₁₀₀ × 5850

= ^{8 × 5850}/₁₀₀

= ⁴⁶⁸⁰⁰/₁₀₀ = $468

Thus, simple interest for 1 year = $468

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $468 × 10 = $4680

Thus, Simple Interest (SI) = $4680

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5850 + $4680

= $10530

Thus, Amount to be paid = $10530 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.

(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 8 years.

(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 7 years.

(4) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.

(6) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 7% simple interest?

(7) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.

(8) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.

(9) How much loan did David borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6750 to clear it?

(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 7 years.