Simple Interest
Math MCQs

Question :    If Susan paid $4234 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3650

Solution & Explanation

Solution

Given,

Amount (A) = $4234

Rate of Simple Interest (R) = 4%

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

$4234 = P (1 + 4% × 4)

⇒ $4234 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4234 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4234 = P (1 + ¹⁶/₁₀₀)

⇒ $4234 = P (^{100 + 16}/₁₀₀)

⇒ $4234 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4234

⇒ P = ⁴²³⁴/_¹¹⁶/100

⇒ P = 4234 × ¹⁰⁰/₁₁₆

⇒ P = ^{4234 × 100}/₁₁₆

⇒ P = ⁴²³⁴⁰⁰/₁₁₆

⇒ P = $3650

Thus, the sum borrowed (P) = $3650 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 4234, then the Principal = ¹⁰⁰/₁₁₆ × 4234

= ^{100 × 4234}/₁₁₆

= ⁴²³⁴⁰⁰/₁₁₆

= 3650

Thus, Principal = $3650

Thus, the sum borrowed = $3650 Answer

Similar Questions

(1) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5576 to clear the loan, then find the time period of the loan.

(2) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 3 years.

(4) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.

(5) In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?

(6) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 8 years.

(7) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 4 years.

(8) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.

(9) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.

(10) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6556 to clear the loan, then find the time period of the loan.