Simple Interest
Math MCQs

Question :    Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 8 years.

Correct Answer  $8346

Solution & Explanation

Solution

Given,

Principal (P) = $5350

Rate of Simple Interest (SI) = 7%

Time (t) = 8 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) = $5350 × 7% × 8

= $5350 ×⁷/₁₀₀ × 8

= ^{5350 × 7 × 8}/₁₀₀

= ^{37450 × 8}/₁₀₀

= ²⁹⁹⁶⁰⁰/₁₀₀

= $2996

Thus, Simple Interest = $2996

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 = $5350 + $2996

= $8346

Thus, Amount to be paid = $8346 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 = $5350

Rate of Simple Interest (SI) or (R) = 7%

And, Time (t) = 8 years

Thus, Amount (A)

= $5350 + ($5350 × 7% × 8)

= $5350 + ($5350 ×⁷/₁₀₀ × 8)

= $5350 + (^{5350 × 7 × 8}/₁₀₀)

= $5350 + (^{37450 × 8}/₁₀₀)

= $5350 + (²⁹⁹⁶⁰⁰/₁₀₀)

= $5350 + $2996 = $8346

Thus, Amount (A) to be paid = $8346 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 $5350, the simple interest in 1 year

= ⁷/₁₀₀ × 5350

= ^{7 × 5350}/₁₀₀

= ³⁷⁴⁵⁰/₁₀₀ = $374.5

Thus, simple interest for 1 year = $374.5

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $374.5 × 8 = $2996

Thus, Simple Interest (SI) = $2996

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5350 + $2996

= $8346

Thus, Amount to be paid = $8346 Answer

Similar Questions

(1) If Barbara borrowed $3550 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 4 years.

(3) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.

(4) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.

(5) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 9% simple interest?

(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 7 years.

(8) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.

(9) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.

(10) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.