Simple Interest
Math MCQs

Question :    If Daniel paid $4428 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4100

Solution & Explanation

Solution

Given,

Amount (A) = $4428

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

$4428 = P (1 + 2% × 4)

⇒ $4428 = P (1 + ²/₁₀₀ × 4)

⇒ $4428 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4428 = P (1 + ⁸/₁₀₀)

⇒ $4428 = P (^{100 + 8}/₁₀₀)

⇒ $4428 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4428

⇒ P = ⁴⁴²⁸/_¹⁰⁸/100

⇒ P = 4428 × ¹⁰⁰/₁₀₈

⇒ P = ^{4428 × 100}/₁₀₈

⇒ P = ⁴⁴²⁸⁰⁰/₁₀₈

⇒ P = $4100

Thus, the sum borrowed (P) = $4100 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 4428, then the Principal = ¹⁰⁰/₁₀₈ × 4428

= ^{100 × 4428}/₁₀₈

= ⁴⁴²⁸⁰⁰/₁₀₈

= 4100

Thus, Principal = $4100

Thus, the sum borrowed = $4100 Answer

Similar Questions

(1) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 4 years.

(2) How much loan did Edward borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9120 to clear it?

(3) If Matthew paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(4) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 4% simple interest?

(5) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 9% simple interest?

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

(7) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.

(8) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7783 to clear the loan, then find the time period of the loan.

(9) How much loan did Betty borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7500 to clear it?

(10) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6267.5 to clear it?