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) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 8% simple interest?

(2) If Jennifer paid $3770 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9348 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 3 years.

(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 7 years.

(6) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 8 years.

(8) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 8 years.

(9) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.

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