Simple Interest
Math MCQs

Question :    Joseph had to pay $3922 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  $3700

Solution & Explanation

Solution

Given,

Amount (A) = $3922

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

$3922 = P (1 + 2% × 3)

⇒ $3922 = P (1 + ²/₁₀₀ × 3)

⇒ $3922 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3922 = P (1 + ⁶/₁₀₀)

⇒ $3922 = P (^{100 + 6}/₁₀₀)

⇒ $3922 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3922

⇒ P = ³⁹²²/_¹⁰⁶/100

⇒ P = 3922 × ¹⁰⁰/₁₀₆

⇒ P = ^{3922 × 100}/₁₀₆

⇒ P = ³⁹²²⁰⁰/₁₀₆

⇒ P = $3700

Thus, the sum borrowed (P) = $3700 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 3922, then the Principal = ¹⁰⁰/₁₀₆ × 3922

= ^{100 × 3922}/₁₀₆

= ³⁹²²⁰⁰/₁₀₆

= 3700

Thus, Principal = $3700

Thus, the sum borrowed = $3700 Answer

Similar Questions

(1) If Sarah paid $4466 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(2) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 7% simple interest?

(4) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 6% simple interest?

(5) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.

(6) David had to pay $3706 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(7) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.

(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.

(9) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.

(10) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.