Simple Interest
Math MCQs

Question :    If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3400

Solution & Explanation

Solution

Given,

Amount (A) = $3672

Rate of Simple Interest (R) = 2%

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

$3672 = P (1 + 2% × 4)

⇒ $3672 = P (1 + ²/₁₀₀ × 4)

⇒ $3672 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3672 = P (1 + ⁸/₁₀₀)

⇒ $3672 = P (^{100 + 8}/₁₀₀)

⇒ $3672 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3672

⇒ P = ³⁶⁷²/_¹⁰⁸/100

⇒ P = 3672 × ¹⁰⁰/₁₀₈

⇒ P = ^{3672 × 100}/₁₀₈

⇒ P = ³⁶⁷²⁰⁰/₁₀₈

⇒ P = $3400

Thus, the sum borrowed (P) = $3400 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 3672, then the Principal = ¹⁰⁰/₁₀₈ × 3672

= ^{100 × 3672}/₁₀₈

= ³⁶⁷²⁰⁰/₁₀₈

= 3400

Thus, Principal = $3400

Thus, the sum borrowed = $3400 Answer

Similar Questions

(1) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9050 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.

(3) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 8 years.

(5) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.

(7) How much loan did Steven borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7260 to clear it?

(8) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.

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

(10) How much loan did Thomas borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6380 to clear it?