Simple Interest
Math MCQs

Question :    If Jessica paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3750

Solution & Explanation

Solution

Given,

Amount (A) = $4200

Rate of Simple Interest (R) = 3%

Time (T) = 4 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

$4200 = P (1 + 3% × 4)

⇒ $4200 = P (1 + ³/₁₀₀ × 4)

⇒ $4200 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4200 = P (1 + ¹²/₁₀₀)

⇒ $4200 = P (^{100 + 12}/₁₀₀)

⇒ $4200 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4200

⇒ P = ⁴²⁰⁰/_¹¹²/100

⇒ P = 4200 × ¹⁰⁰/₁₁₂

⇒ P = ^{4200 × 100}/₁₁₂

⇒ P = ⁴²⁰⁰⁰⁰/₁₁₂

⇒ 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 3 = 12

Thus, simple interest for 4 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 4200, then the Principal = ¹⁰⁰/₁₁₂ × 4200

= ^{100 × 4200}/₁₁₂

= ⁴²⁰⁰⁰⁰/₁₁₂

= 3750

Thus, Principal = $3750

Thus, the sum borrowed = $3750 Answer

Similar Questions

(1) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 7 years.

(2) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 7% simple interest?

(4) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 10% simple interest?

(5) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.

(6) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 2% simple interest?

(7) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.

(8) If Matthew paid $4704 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 7 years.