Simple Interest
Math MCQs

Question :    Sarah had to pay $4081 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $3850

Solution & Explanation

Solution

Given,

Amount (A) = $4081

Rate of Simple Interest (R) = 2%

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

$4081 = P (1 + 2% × 3)

⇒ $4081 = P (1 + ²/₁₀₀ × 3)

⇒ $4081 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $4081 = P (1 + ⁶/₁₀₀)

⇒ $4081 = P (^{100 + 6}/₁₀₀)

⇒ $4081 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $4081

⇒ P = ⁴⁰⁸¹/_¹⁰⁶/100

⇒ P = 4081 × ¹⁰⁰/₁₀₆

⇒ P = ^{4081 × 100}/₁₀₆

⇒ P = ⁴⁰⁸¹⁰⁰/₁₀₆

⇒ P = $3850

Thus, the sum borrowed (P) = $3850 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 4081, then the Principal = ¹⁰⁰/₁₀₆ × 4081

= ^{100 × 4081}/₁₀₆

= ⁴⁰⁸¹⁰⁰/₁₀₆

= 3850

Thus, Principal = $3850

Thus, the sum borrowed = $3850 Answer

Similar Questions

(1) How much loan did Daniel borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7320 to clear it?

(2) If Thomas paid $4256 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.

(4) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.

(5) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.

(6) How much loan did Edward borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9500 to clear it?

(7) What amount does John have to pay after 6 years if he takes a loan of $3200 at 2% simple interest?

(8) How much loan did James borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6000 to clear it?

(9) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?

(10) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.