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) How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?

(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 7 years.

(3) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.

(4) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?

(5) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 4 years.

(6) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 10% simple interest?

(7) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if William borrowed a sum of $3250 at a 5% simple interest?

(9) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 3 years.

(10) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.