Simple Interest
Math MCQs

Question :    If Karen paid $4740 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3950

Solution & Explanation

Solution

Given,

Amount (A) = $4740

Rate of Simple Interest (R) = 5%

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

$4740 = P (1 + 5% × 4)

⇒ $4740 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4740 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4740 = P (1 + ²⁰/₁₀₀)

⇒ $4740 = P (^{100 + 20}/₁₀₀)

⇒ $4740 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4740

⇒ P = ⁴⁷⁴⁰/_¹²⁰/100

⇒ P = 4740 × ¹⁰⁰/₁₂₀

⇒ P = ^{4740 × 100}/₁₂₀

⇒ P = ⁴⁷⁴⁰⁰⁰/₁₂₀

⇒ 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 20

Thus, simple interest for 4 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 4740, then the Principal = ¹⁰⁰/₁₂₀ × 4740

= ^{100 × 4740}/₁₂₀

= ⁴⁷⁴⁰⁰⁰/₁₂₀

= 3950

Thus, Principal = $3950

Thus, the sum borrowed = $3950 Answer

Similar Questions

(1) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 5% simple interest.

(3) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 6% simple interest?

(4) If Charles paid $4212 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) If David paid $3944 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.

(7) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?

(8) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6240 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) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 4 years.