Simple Interest
Math MCQs

Question :    If Patricia paid $3654 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3150

Solution & Explanation

Solution

Given,

Amount (A) = $3654

Rate of Simple Interest (R) = 4%

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

$3654 = P (1 + 4% × 4)

⇒ $3654 = P (1 + ⁴/₁₀₀ × 4)

⇒ $3654 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $3654 = P (1 + ¹⁶/₁₀₀)

⇒ $3654 = P (^{100 + 16}/₁₀₀)

⇒ $3654 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $3654

⇒ P = ³⁶⁵⁴/_¹¹⁶/100

⇒ P = 3654 × ¹⁰⁰/₁₁₆

⇒ P = ^{3654 × 100}/₁₁₆

⇒ P = ³⁶⁵⁴⁰⁰/₁₁₆

⇒ P = $3150

Thus, the sum borrowed (P) = $3150 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 3654, then the Principal = ¹⁰⁰/₁₁₆ × 3654

= ^{100 × 3654}/₁₁₆

= ³⁶⁵⁴⁰⁰/₁₁₆

= 3150

Thus, Principal = $3150

Thus, the sum borrowed = $3150 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.

(2) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 3 years.

(3) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 9% simple interest?

(4) 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?

(5) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.

(6) Joshua had to pay $5488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) 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?

(8) Karen had to pay $4424 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 2% simple interest?

(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 8 years.