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) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 10% simple interest?

(2) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.

(3) How much loan did Christopher borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6600 to clear it?

(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 4 years.

(5) If Elizabeth paid $4140 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) If Christopher paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) Paul had to pay $5123 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 6% simple interest?

(9) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 7 years.

(10) Lisa had to pay $4536 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.