Simple Interest
Math MCQs

Question :    Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 7 years.

Correct Answer  $7956

Solution & Explanation

Solution

Given,

Principal (P) = $5100

Rate of Simple Interest (SI) = 8%

Time (t) = 7 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) = $5100 × 8% × 7

= $5100 ×⁸/₁₀₀ × 7

= ^{5100 × 8 × 7}/₁₀₀

= ^{40800 × 7}/₁₀₀

= ²⁸⁵⁶⁰⁰/₁₀₀

= $2856

Thus, Simple Interest = $2856

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 = $5100 + $2856

= $7956

Thus, Amount to be paid = $7956 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 = $5100

Rate of Simple Interest (SI) or (R) = 8%

And, Time (t) = 7 years

Thus, Amount (A)

= $5100 + ($5100 × 8% × 7)

= $5100 + ($5100 ×⁸/₁₀₀ × 7)

= $5100 + (^{5100 × 8 × 7}/₁₀₀)

= $5100 + (^{40800 × 7}/₁₀₀)

= $5100 + (²⁸⁵⁶⁰⁰/₁₀₀)

= $5100 + $2856 = $7956

Thus, Amount (A) to be paid = $7956 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 $5100, the simple interest in 1 year

= ⁸/₁₀₀ × 5100

= ^{8 × 5100}/₁₀₀

= ⁴⁰⁸⁰⁰/₁₀₀ = $408

Thus, simple interest for 1 year = $408

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $408 × 7 = $2856

Thus, Simple Interest (SI) = $2856

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5100 + $2856

= $7956

Thus, Amount to be paid = $7956 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.

(2) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.

(3) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 3 years.

(4) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 3 years.

(5) If Steven paid $5336 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 2% simple interest?

(7) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?

(8) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.

(9) How much loan did Donna borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7535 to clear it?

(10) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.