Simple Interest
Math MCQs

Question :    If Joseph paid $4440 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3700

Solution & Explanation

Solution

Given,

Amount (A) = $4440

Rate of Simple Interest (R) = 5%

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

$4440 = P (1 + 5% × 4)

⇒ $4440 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4440 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4440 = P (1 + ²⁰/₁₀₀)

⇒ $4440 = P (^{100 + 20}/₁₀₀)

⇒ $4440 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4440

⇒ P = ⁴⁴⁴⁰/_¹²⁰/100

⇒ P = 4440 × ¹⁰⁰/₁₂₀

⇒ P = ^{4440 × 100}/₁₂₀

⇒ P = ⁴⁴⁴⁰⁰⁰/₁₂₀

⇒ 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 20

Thus, simple interest for 4 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 4440, then the Principal = ¹⁰⁰/₁₂₀ × 4440

= ^{100 × 4440}/₁₂₀

= ⁴⁴⁴⁰⁰⁰/₁₂₀

= 3700

Thus, Principal = $3700

Thus, the sum borrowed = $3700 Answer

Similar Questions

(1) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $14000 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 3 years.

(3) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.

(4) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 7% simple interest?

(6) How much loan did Ashley borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7860 to clear it?

(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 3 years.

(8) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.

(9) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 5% simple interest?

(10) How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?