Simple Interest
Math MCQs

Question :    If Michael paid $3564 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3300

Solution & Explanation

Solution

Given,

Amount (A) = $3564

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

$3564 = P (1 + 2% × 4)

⇒ $3564 = P (1 + ²/₁₀₀ × 4)

⇒ $3564 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3564 = P (1 + ⁸/₁₀₀)

⇒ $3564 = P (^{100 + 8}/₁₀₀)

⇒ $3564 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3564

⇒ P = ³⁵⁶⁴/_¹⁰⁸/100

⇒ P = 3564 × ¹⁰⁰/₁₀₈

⇒ P = ^{3564 × 100}/₁₀₈

⇒ P = ³⁵⁶⁴⁰⁰/₁₀₈

⇒ P = $3300

Thus, the sum borrowed (P) = $3300 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 3564, then the Principal = ¹⁰⁰/₁₀₈ × 3564

= ^{100 × 3564}/₁₀₈

= ³⁵⁶⁴⁰⁰/₁₀₈

= 3300

Thus, Principal = $3300

Thus, the sum borrowed = $3300 Answer

Similar Questions

(1) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?

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

(3) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.

(4) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 7 years.

(6) If Paul paid $5452 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) If Susan paid $4088 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 7 years.

(9) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.

(10) If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.