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) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.

(2) If Linda paid $3752 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?

(4) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.

(5) What amount does John have to pay after 6 years if he takes a loan of $3200 at 7% simple interest?

(6) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) Calculate the amount due if Charles borrowed a sum of $3900 at 4% simple interest for 3 years.

(8) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9020 to clear the loan, then find the time period of the loan.

(9) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.