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) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.

(2) If Joseph paid $4144 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 4 years.

(5) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 3 years.

(6) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.

(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 4 years.

(8) John had to pay $3392 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 8 years.

(10) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 9% simple interest?