Simple Interest
Math MCQs

Question :    If Anthony paid $4644 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4300

Solution & Explanation

Solution

Given,

Amount (A) = $4644

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

$4644 = P (1 + 2% × 4)

⇒ $4644 = P (1 + ²/₁₀₀ × 4)

⇒ $4644 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4644 = P (1 + ⁸/₁₀₀)

⇒ $4644 = P (^{100 + 8}/₁₀₀)

⇒ $4644 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4644

⇒ P = ⁴⁶⁴⁴/_¹⁰⁸/100

⇒ P = 4644 × ¹⁰⁰/₁₀₈

⇒ P = ^{4644 × 100}/₁₀₈

⇒ P = ⁴⁶⁴⁴⁰⁰/₁₀₈

⇒ P = $4300

Thus, the sum borrowed (P) = $4300 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 4644, then the Principal = ¹⁰⁰/₁₀₈ × 4644

= ^{100 × 4644}/₁₀₈

= ⁴⁶⁴⁴⁰⁰/₁₀₈

= 4300

Thus, Principal = $4300

Thus, the sum borrowed = $4300 Answer

Similar Questions

(1) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.

(2) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 4 years.

(3) Nancy had to pay $4648 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) How much loan did Ronald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9375 to clear it?

(5) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?

(6) If Donald paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) If Susan paid $4234 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 3% simple interest?

(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 4 years.

(10) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.