Simple Interest
Math MCQs

Question :  ( 1 of 10 )  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) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.

(2) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 7 years.

(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 3 years.

(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 8 years.

(6) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 7 years.

(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 8 years.

(9) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 3% simple interest?

(10) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 10% simple interest?