Simple Interest
Math MCQs

Question :    Richard had to pay $4032 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  $3600

Solution & Explanation

Solution

Given,

Amount (A) = $4032

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

$4032 = P (1 + 4% × 3)

⇒ $4032 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4032 = P (1 + ^{4 × 3}/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 = 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 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) How much loan did Ronald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9375 to clear it?

(2) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8528 to clear the loan, then find the time period of the loan.

(3) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 3 years.

(5) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

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

(7) If Kenneth paid $6000 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(8) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.

(9) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 4% simple interest?

(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 7 years.