Simple Interest
Math MCQs

Question :    If Joseph paid $4144 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3700

Solution & Explanation

Solution

Given,

Amount (A) = $4144

Rate of Simple Interest (R) = 3%

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

$4144 = P (1 + 3% × 4)

⇒ $4144 = P (1 + ³/₁₀₀ × 4)

⇒ $4144 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4144 = P (1 + ¹²/₁₀₀)

⇒ $4144 = P (^{100 + 12}/₁₀₀)

⇒ $4144 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4144

⇒ P = ⁴¹⁴⁴/_¹¹²/100

⇒ P = 4144 × ¹⁰⁰/₁₁₂

⇒ P = ^{4144 × 100}/₁₁₂

⇒ P = ⁴¹⁴⁴⁰⁰/₁₁₂

⇒ P = $3700

Thus, the sum borrowed (P) = $3700 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 12

Thus, simple interest for 4 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 4144, then the Principal = ¹⁰⁰/₁₁₂ × 4144

= ^{100 × 4144}/₁₁₂

= ⁴¹⁴⁴⁰⁰/₁₁₂

= 3700

Thus, Principal = $3700

Thus, the sum borrowed = $3700 Answer

Similar Questions

(1) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.

(2) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?

(3) Emily had to pay $5320 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 4 years.

(6) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 4 years.

(7) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 3 years.

(8) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 7% simple interest?

(9) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?

(10) Nancy had to pay $4523.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.