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) Matthew had to pay $4704 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 7 years.

(4) What amount does James have to pay after 5 years if he takes a loan of $3000 at 4% simple interest?

(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 4 years.

(6) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.

(7) What amount does James have to pay after 5 years if he takes a loan of $3000 at 6% simple interest?

(8) If Nancy paid $4648 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) If Andrew paid $5184 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.