Simple Interest
Math MCQs

Question :    Joseph had to pay $4144 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $3700

Solution & Explanation

Solution

Given,

Amount (A) = $4144

Rate of Simple Interest (R) = 4%

Time (T) = 3 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 + 4% × 3)

⇒ $4144 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4144 = P (1 + ^{4 × 3}/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 = 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 4 = 12

Thus, simple interest for 3 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) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 3 years.

(3) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.

(4) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 3 years.

(5) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.

(6) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(7) If Richard paid $3888 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 10% simple interest?

(9) In how much time a principal of $3200 will amount to $3392 at a simple interest of 3% per annum?

(10) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.