Simple Interest
Math MCQs

Question :    If Richard paid $4032 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3600

Solution & Explanation

Solution

Given,

Amount (A) = $4032

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

$4032 = P (1 + 3% × 4)

⇒ $4032 = P (1 + ³/₁₀₀ × 4)

⇒ $4032 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4032 = P (1 + ¹²/₁₀₀)

⇒ $4032 = P (^{100 + 12}/₁₀₀)

⇒ $4032 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4032

⇒ P = ⁴⁰³²/_¹¹²/100

⇒ P = 4032 × ¹⁰⁰/₁₁₂

⇒ P = ^{4032 × 100}/₁₁₂

⇒ P = ⁴⁰³²⁰⁰/₁₁₂

⇒ P = $3600

Thus, the sum borrowed (P) = $3600 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 4032, then the Principal = ¹⁰⁰/₁₁₂ × 4032

= ^{100 × 4032}/₁₁₂

= ⁴⁰³²⁰⁰/₁₁₂

= 3600

Thus, Principal = $3600

Thus, the sum borrowed = $3600 Answer

Similar Questions

(1) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.

(2) Jennifer had to pay $3445 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 3 years.

(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 4 years.

(5) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 8% simple interest?

(6) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 2% simple interest?

(7) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(8) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 3 years.

(10) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 4% simple interest?