Simple Interest
Math MCQs

Question :    Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 7 years.

Correct Answer  $7748

Solution & Explanation

Solution

Given,

Principal (P) = $5200

Rate of Simple Interest (SI) = 7%

Time (t) = 7 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) = $5200 × 7% × 7

= $5200 ×⁷/₁₀₀ × 7

= ^{5200 × 7 × 7}/₁₀₀

= ^{36400 × 7}/₁₀₀

= ²⁵⁴⁸⁰⁰/₁₀₀

= $2548

Thus, Simple Interest = $2548

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 = $5200 + $2548

= $7748

Thus, Amount to be paid = $7748 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 = $5200

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

And, Time (t) = 7 years

Thus, Amount (A)

= $5200 + ($5200 × 7% × 7)

= $5200 + ($5200 ×⁷/₁₀₀ × 7)

= $5200 + (^{5200 × 7 × 7}/₁₀₀)

= $5200 + (^{36400 × 7}/₁₀₀)

= $5200 + (²⁵⁴⁸⁰⁰/₁₀₀)

= $5200 + $2548 = $7748

Thus, Amount (A) to be paid = $7748 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 $5200, the simple interest in 1 year

= ⁷/₁₀₀ × 5200

= ^{7 × 5200}/₁₀₀

= ³⁶⁴⁰⁰/₁₀₀ = $364

Thus, simple interest for 1 year = $364

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $364 × 7 = $2548

Thus, Simple Interest (SI) = $2548

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5200 + $2548

= $7748

Thus, Amount to be paid = $7748 Answer

Similar Questions

(1) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 3 years.

(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 8 years.

(3) If Emily paid $5320 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(4) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(5) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.

(6) Nancy had to pay $4399 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.

(8) If Christopher borrowed $4000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(9) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 8 years.