Simple Interest
Math MCQs

Question :    If Karen paid $4424 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3950

Solution & Explanation

Solution

Given,

Amount (A) = $4424

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

$4424 = P (1 + 3% × 4)

⇒ $4424 = P (1 + ³/₁₀₀ × 4)

⇒ $4424 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4424 = P (1 + ¹²/₁₀₀)

⇒ $4424 = P (^{100 + 12}/₁₀₀)

⇒ $4424 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4424

⇒ P = ⁴⁴²⁴/_¹¹²/100

⇒ P = 4424 × ¹⁰⁰/₁₁₂

⇒ P = ^{4424 × 100}/₁₁₂

⇒ P = ⁴⁴²⁴⁰⁰/₁₁₂

⇒ P = $3950

Thus, the sum borrowed (P) = $3950 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 4424, then the Principal = ¹⁰⁰/₁₁₂ × 4424

= ^{100 × 4424}/₁₁₂

= ⁴⁴²⁴⁰⁰/₁₁₂

= 3950

Thus, Principal = $3950

Thus, the sum borrowed = $3950 Answer

Similar Questions

(1) How much loan did Donald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8125 to clear it?

(2) What amount does David have to pay after 6 years if he takes a loan of $3400 at 5% simple interest?

(3) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 4% simple interest?

(4) In how much time a principal of $3000 will amount to $3450 at a simple interest of 3% per annum?

(5) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.

(6) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.

(7) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.

(8) How much loan did Donald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7475 to clear it?

(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 7 years.

(10) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5960 to clear the loan, then find the time period of the loan.