Simple Interest
Math MCQs

Question :    Steven had to pay $5152 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  $4600

Solution & Explanation

Solution

Given,

Amount (A) = $5152

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

$5152 = P (1 + 4% × 3)

⇒ $5152 = P (1 + ⁴/₁₀₀ × 3)

⇒ $5152 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $5152 = P (1 + ¹²/₁₀₀)

⇒ $5152 = P (^{100 + 12}/₁₀₀)

⇒ $5152 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5152

⇒ P = ⁵¹⁵²/_¹¹²/100

⇒ P = 5152 × ¹⁰⁰/₁₁₂

⇒ P = ^{5152 × 100}/₁₁₂

⇒ P = ⁵¹⁵²⁰⁰/₁₁₂

⇒ P = $4600

Thus, the sum borrowed (P) = $4600 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 5152, then the Principal = ¹⁰⁰/₁₁₂ × 5152

= ^{100 × 5152}/₁₁₂

= ⁵¹⁵²⁰⁰/₁₁₂

= 4600

Thus, Principal = $4600

Thus, the sum borrowed = $4600 Answer

Similar Questions

(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.

(2) 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?

(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 7 years.

(4) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 7 years.

(6) If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) What amount does John have to pay after 5 years if he takes a loan of $3200 at 4% simple interest?

(8) How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?

(9) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 4 years.

(10) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.