Simple Interest
Math MCQs

Question :    Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 7 years.

Correct Answer  $10115

Solution & Explanation

Solution

Given,

Principal (P) = $5950

Rate of Simple Interest (SI) = 10%

Time (t) = 7 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% × 7

= $5950 ×¹⁰/₁₀₀ × 7

= ^{5950 × 10 × 7}/₁₀₀

= ^{59500 × 7}/₁₀₀

= ⁴¹⁶⁵⁰⁰/₁₀₀

= $4165

Thus, Simple Interest = $4165

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 + $4165

= $10115

Thus, Amount to be paid = $10115 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) = 7 years

Thus, Amount (A)

= $5950 + ($5950 × 10% × 7)

= $5950 + ($5950 ×¹⁰/₁₀₀ × 7)

= $5950 + (^{5950 × 10 × 7}/₁₀₀)

= $5950 + (^{59500 × 7}/₁₀₀)

= $5950 + (⁴¹⁶⁵⁰⁰/₁₀₀)

= $5950 + $4165 = $10115

Thus, Amount (A) to be paid = $10115 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 7 years

= Simple interest for 1 year × 7

= $595 × 7 = $4165

Thus, Simple Interest (SI) = $4165

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5950 + $4165

= $10115

Thus, Amount to be paid = $10115 Answer

Similar Questions

(1) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.

(2) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10660 to clear the loan, then find the time period of the loan.

(3) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?

(4) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 6% simple interest?

(6) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.

(7) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?

(8) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.

(9) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.

(10) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.