Simple Interest
Math MCQs

Question :    Andrew had to pay $5376 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  $4800

Solution & Explanation

Solution

Given,

Amount (A) = $5376

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

$5376 = P (1 + 4% × 3)

⇒ $5376 = P (1 + ⁴/₁₀₀ × 3)

⇒ $5376 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $5376 = P (1 + ¹²/₁₀₀)

⇒ $5376 = P (^{100 + 12}/₁₀₀)

⇒ $5376 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5376

⇒ P = ⁵³⁷⁶/_¹¹²/100

⇒ P = 5376 × ¹⁰⁰/₁₁₂

⇒ P = ^{5376 × 100}/₁₁₂

⇒ P = ⁵³⁷⁶⁰⁰/₁₁₂

⇒ P = $4800

Thus, the sum borrowed (P) = $4800 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 5376, then the Principal = ¹⁰⁰/₁₁₂ × 5376

= ^{100 × 5376}/₁₁₂

= ⁵³⁷⁶⁰⁰/₁₁₂

= 4800

Thus, Principal = $4800

Thus, the sum borrowed = $4800 Answer

Similar Questions

(1) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 3 years.

(2) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(3) If William borrowed $3500 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(4) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.

(5) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?

(6) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 3% simple interest?

(7) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.

(8) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 5% simple interest?

(9) Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?