Simple Interest
Math MCQs

Question :    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.

Correct Answer  $3650

Solution & Explanation

Solution

Given,

Amount (A) = $4234

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

$4234 = P (1 + 4% × 4)

⇒ $4234 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4234 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4234 = P (1 + ¹⁶/₁₀₀)

⇒ $4234 = P (^{100 + 16}/₁₀₀)

⇒ $4234 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4234

⇒ P = ⁴²³⁴/_¹¹⁶/100

⇒ P = 4234 × ¹⁰⁰/₁₁₆

⇒ P = ^{4234 × 100}/₁₁₆

⇒ P = ⁴²³⁴⁰⁰/₁₁₆

⇒ P = $3650

Thus, the sum borrowed (P) = $3650 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 4234, then the Principal = ¹⁰⁰/₁₁₆ × 4234

= ^{100 × 4234}/₁₁₆

= ⁴²³⁴⁰⁰/₁₁₆

= 3650

Thus, Principal = $3650

Thus, the sum borrowed = $3650 Answer

Similar Questions

(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.

(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 8 years.

(3) Donald had to pay $4905 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(4) If Lisa paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 7 years.

(6) Calculate the amount due if Susan borrowed a sum of $3650 at 8% simple interest for 3 years.

(7) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9180 to clear it?

(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 8 years.

(9) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.

(10) Robert had to pay $3472 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.