Simple Interest
Math MCQs

Question :    If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3000

Solution & Explanation

Solution

Given,

Amount (A) = $3360

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

$3360 = P (1 + 3% × 4)

⇒ $3360 = P (1 + ³/₁₀₀ × 4)

⇒ $3360 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $3360 = P (1 + ¹²/₁₀₀)

⇒ $3360 = P (^{100 + 12}/₁₀₀)

⇒ $3360 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3360

⇒ P = ³³⁶⁰/_¹¹²/100

⇒ P = 3360 × ¹⁰⁰/₁₁₂

⇒ P = ^{3360 × 100}/₁₁₂

⇒ P = ³³⁶⁰⁰⁰/₁₁₂

⇒ P = $3000

Thus, the sum borrowed (P) = $3000 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 3360, then the Principal = ¹⁰⁰/₁₁₂ × 3360

= ^{100 × 3360}/₁₁₂

= ³³⁶⁰⁰⁰/₁₁₂

= 3000

Thus, Principal = $3000

Thus, the sum borrowed = $3000 Answer

Similar Questions

(1) How much loan did Joseph borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6270 to clear it?

(2) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $6936 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.

(4) How much loan did Matthew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7750 to clear it?

(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 4 years.

(6) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?

(7) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.

(8) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.

(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 8 years.