Simple Interest
Math MCQs

Question :    Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 8 years.

Correct Answer  $10710

Solution & Explanation

Solution

Given,

Principal (P) = $5950

Rate of Simple Interest (SI) = 10%

Time (t) = 8 years

Thus, Amount (A) = ?

The Rate of Interest is always calculated per annum, i.e. per year.

Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $5950 × 10% × 8

= $5950 ×¹⁰/₁₀₀ × 8

= ^{5950 × 10 × 8}/₁₀₀

= ^{59500 × 8}/₁₀₀

= ⁴⁷⁶⁰⁰⁰/₁₀₀

= $4760

Thus, Simple Interest = $4760

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 = $5950 + $4760

= $10710

Thus, Amount to be paid = $10710 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 = $5950

Rate of Simple Interest (SI) or (R) = 10%

And, Time (t) = 8 years

Thus, Amount (A)

= $5950 + ($5950 × 10% × 8)

= $5950 + ($5950 ×¹⁰/₁₀₀ × 8)

= $5950 + (^{5950 × 10 × 8}/₁₀₀)

= $5950 + (^{59500 × 8}/₁₀₀)

= $5950 + (⁴⁷⁶⁰⁰⁰/₁₀₀)

= $5950 + $4760 = $10710

Thus, Amount (A) to be paid = $10710 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 10%

This, means, $10 per $100 per year

∵ For $100, the simple interest for 1 year = $10

∴ For $1, the simple interest for 1 year = ¹⁰/₁₀₀

∴ For $5950, the simple interest in 1 year

= ¹⁰/₁₀₀ × 5950

= ^{10 × 5950}/₁₀₀

= ⁵⁹⁵⁰⁰/₁₀₀ = $595

Thus, simple interest for 1 year = $595

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $595 × 8 = $4760

Thus, Simple Interest (SI) = $4760

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5950 + $4760

= $10710

Thus, Amount to be paid = $10710 Answer

Similar Questions

(1) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.

(2) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.

(3) Daniel had to pay $4469 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(4) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7897 to clear the loan, then find the time period of the loan.

(5) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.

(7) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.

(9) What amount does John have to pay after 5 years if he takes a loan of $3200 at 4% simple interest?

(10) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.