Simple Interest
Math MCQs

Question :    If Lisa paid $4374 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4050

Solution & Explanation

Solution

Given,

Amount (A) = $4374

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

$4374 = P (1 + 2% × 4)

⇒ $4374 = P (1 + ²/₁₀₀ × 4)

⇒ $4374 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4374 = P (1 + ⁸/₁₀₀)

⇒ $4374 = P (^{100 + 8}/₁₀₀)

⇒ $4374 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4374

⇒ P = ⁴³⁷⁴/_¹⁰⁸/100

⇒ P = 4374 × ¹⁰⁰/₁₀₈

⇒ P = ^{4374 × 100}/₁₀₈

⇒ P = ⁴³⁷⁴⁰⁰/₁₀₈

⇒ P = $4050

Thus, the sum borrowed (P) = $4050 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 4374, then the Principal = ¹⁰⁰/₁₀₈ × 4374

= ^{100 × 4374}/₁₀₈

= ⁴³⁷⁴⁰⁰/₁₀₈

= 4050

Thus, Principal = $4050

Thus, the sum borrowed = $4050 Answer

Similar Questions

(1) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 7 years.

(2) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 2% simple interest?

(3) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.

(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 7 years.

(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 8 years.

(7) If Linda paid $3886 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.

(9) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 2% simple interest?

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