Simple Interest
Math MCQs

Question :    Jessica had to pay $3975 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $3750

Solution & Explanation

Solution

Given,

Amount (A) = $3975

Rate of Simple Interest (R) = 2%

Time (T) = 3 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$3975 = P (1 + 2% × 3)

⇒ $3975 = P (1 + ²/₁₀₀ × 3)

⇒ $3975 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3975 = P (1 + ⁶/₁₀₀)

⇒ $3975 = P (^{100 + 6}/₁₀₀)

⇒ $3975 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3975

⇒ P = ³⁹⁷⁵/_¹⁰⁶/100

⇒ P = 3975 × ¹⁰⁰/₁₀₆

⇒ P = ^{3975 × 100}/₁₀₆

⇒ P = ³⁹⁷⁵⁰⁰/₁₀₆

⇒ P = $3750

Thus, the sum borrowed (P) = $3750 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

Calculation of the Amount

Since, in the question, time = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 3975, then the Principal = ¹⁰⁰/₁₀₆ × 3975

= ^{100 × 3975}/₁₀₆

= ³⁹⁷⁵⁰⁰/₁₀₆

= 3750

Thus, Principal = $3750

Thus, the sum borrowed = $3750 Answer

Similar Questions

(1) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 10% simple interest?

(2) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.

(3) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?

(4) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 6% simple interest?

(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 8 years.

(6) How much loan did Joshua borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8280 to clear it?

(7) How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?

(8) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 5% simple interest.

(9) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.