Simple Interest
Math MCQs

Question :  ( 1 of 10 )  If Joshua paid $5488 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4900

Solution & Explanation

Solution

Given,

Amount (A) = $5488

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

$5488 = P (1 + 3% × 4)

⇒ $5488 = P (1 + ³/₁₀₀ × 4)

⇒ $5488 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $5488 = P (1 + ¹²/₁₀₀)

⇒ $5488 = P (^{100 + 12}/₁₀₀)

⇒ $5488 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5488

⇒ P = ⁵⁴⁸⁸/_¹¹²/100

⇒ P = 5488 × ¹⁰⁰/₁₁₂

⇒ P = ^{5488 × 100}/₁₁₂

⇒ P = ⁵⁴⁸⁸⁰⁰/₁₁₂

⇒ P = $4900

Thus, the sum borrowed (P) = $4900 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 5488, then the Principal = ¹⁰⁰/₁₁₂ × 5488

= ^{100 × 5488}/₁₁₂

= ⁵⁴⁸⁸⁰⁰/₁₁₂

= 4900

Thus, Principal = $4900

Thus, the sum borrowed = $4900 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.

(2) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.

(3) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?

(4) How much loan did Michael borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6095 to clear it?

(5) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 7% simple interest?

(6) How much loan did William borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6050 to clear it?

(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 7 years.

(8) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.

(9) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12800 to clear the loan, then find the time period of the loan.

(10) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?