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

(2) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.

(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 8 years.

(4) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 8% simple interest?

(5) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?

(6) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 9% simple interest?

(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 8 years.

(8) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 4 years.

(10) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.