Simple Interest
Math MCQs

Question :    If Kimberly paid $5208 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4650

Solution & Explanation

Solution

Given,

Amount (A) = $5208

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

$5208 = P (1 + 3% × 4)

⇒ $5208 = P (1 + ³/₁₀₀ × 4)

⇒ $5208 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $5208 = P (1 + ¹²/₁₀₀)

⇒ $5208 = P (^{100 + 12}/₁₀₀)

⇒ $5208 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5208

⇒ P = ⁵²⁰⁸/_¹¹²/100

⇒ P = 5208 × ¹⁰⁰/₁₁₂

⇒ P = ^{5208 × 100}/₁₁₂

⇒ P = ⁵²⁰⁸⁰⁰/₁₁₂

⇒ P = $4650

Thus, the sum borrowed (P) = $4650 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 5208, then the Principal = ¹⁰⁰/₁₁₂ × 5208

= ^{100 × 5208}/₁₁₂

= ⁵²⁰⁸⁰⁰/₁₁₂

= 4650

Thus, Principal = $4650

Thus, the sum borrowed = $4650 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) How much loan did Thomas borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6380 to clear it?

(3) How much loan did Nancy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7687.5 to clear it?

(4) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.

(5) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.

(6) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.

(7) In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?

(8) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.

(9) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(10) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 4% simple interest?