Simple Interest
Math MCQs

Question :    Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 8 years.

Correct Answer  $8736

Solution & Explanation

Solution

Given,

Principal (P) = $5600

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) = $5600 × 7% × 8

= $5600 ×⁷/₁₀₀ × 8

= ^{5600 × 7 × 8}/₁₀₀

= ^{39200 × 8}/₁₀₀

= ³¹³⁶⁰⁰/₁₀₀

= $3136

Thus, Simple Interest = $3136

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 = $5600 + $3136

= $8736

Thus, Amount to be paid = $8736 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 = $5600

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

And, Time (t) = 8 years

Thus, Amount (A)

= $5600 + ($5600 × 7% × 8)

= $5600 + ($5600 ×⁷/₁₀₀ × 8)

= $5600 + (^{5600 × 7 × 8}/₁₀₀)

= $5600 + (^{39200 × 8}/₁₀₀)

= $5600 + (³¹³⁶⁰⁰/₁₀₀)

= $5600 + $3136 = $8736

Thus, Amount (A) to be paid = $8736 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 $5600, the simple interest in 1 year

= ⁷/₁₀₀ × 5600

= ^{7 × 5600}/₁₀₀

= ³⁹²⁰⁰/₁₀₀ = $392

Thus, simple interest for 1 year = $392

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $392 × 8 = $3136

Thus, Simple Interest (SI) = $3136

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5600 + $3136

= $8736

Thus, Amount to be paid = $8736 Answer

Similar Questions

(1) What amount does William have to pay after 5 years if he takes a loan of $3500 at 10% simple interest?

(2) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 4 years.

(3) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.

(4) 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.

(5) Robert had to pay $3565 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 4 years.

(7) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.

(9) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 3 years.

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