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) How much loan did Michelle borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7645 to clear it?

(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 7 years.

(3) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.

(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 2% simple interest?

(5) How much loan did Edward borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8360 to clear it?

(6) How much loan did Jacob borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9600 to clear it?

(7) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 3% simple interest?

(8) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7975 to clear it?

(9) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.

(10) What amount does David have to pay after 5 years if he takes a loan of $3400 at 9% simple interest?