Simple Interest
Math MCQs

Question :    Thomas had to pay $4256 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  $3800

Solution & Explanation

Solution

Given,

Amount (A) = $4256

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

$4256 = P (1 + 4% × 3)

⇒ $4256 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4256 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $4256 = P (1 + ¹²/₁₀₀)

⇒ $4256 = P (^{100 + 12}/₁₀₀)

⇒ $4256 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4256

⇒ P = ⁴²⁵⁶/_¹¹²/100

⇒ P = 4256 × ¹⁰⁰/₁₁₂

⇒ P = ^{4256 × 100}/₁₁₂

⇒ P = ⁴²⁵⁶⁰⁰/₁₁₂

⇒ P = $3800

Thus, the sum borrowed (P) = $3800 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 4256, then the Principal = ¹⁰⁰/₁₁₂ × 4256

= ^{100 × 4256}/₁₁₂

= ⁴²⁵⁶⁰⁰/₁₁₂

= 3800

Thus, Principal = $3800

Thus, the sum borrowed = $3800 Answer

Similar Questions

(1) How much loan did Joshua borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7590 to clear it?

(2) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 5% simple interest?

(3) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 5% simple interest?

(4) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6037.5 to clear it?

(5) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.

(6) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8432 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 4 years.

(8) William had to pay $4025 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 8 years.

(10) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.