Simple Interest
Math MCQs

Question :    If John paid $3456 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3200

Solution & Explanation

Solution

Given,

Amount (A) = $3456

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

$3456 = P (1 + 2% × 4)

⇒ $3456 = P (1 + ²/₁₀₀ × 4)

⇒ $3456 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3456 = P (1 + ⁸/₁₀₀)

⇒ $3456 = P (^{100 + 8}/₁₀₀)

⇒ $3456 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3456

⇒ P = ³⁴⁵⁶/_¹⁰⁸/100

⇒ P = 3456 × ¹⁰⁰/₁₀₈

⇒ P = ^{3456 × 100}/₁₀₈

⇒ P = ³⁴⁵⁶⁰⁰/₁₀₈

⇒ P = $3200

Thus, the sum borrowed (P) = $3200 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 3456, then the Principal = ¹⁰⁰/₁₀₈ × 3456

= ^{100 × 3456}/₁₀₈

= ³⁴⁵⁶⁰⁰/₁₀₈

= 3200

Thus, Principal = $3200

Thus, the sum borrowed = $3200 Answer

Similar Questions

(1) Calculate the amount due if Linda borrowed a sum of $3350 at 6% simple interest for 4 years.

(2) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5960 to clear the loan, then find the time period of the loan.

(3) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 8% simple interest?

(4) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 8% simple interest?

(6) How much loan did Lisa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7562.5 to clear it?

(7) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 7% simple interest?

(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 8 years.

(9) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.