Simple Interest
Math MCQs

Question :    Emily had to pay $5035 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  $4750

Solution & Explanation

Solution

Given,

Amount (A) = $5035

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

$5035 = P (1 + 2% × 3)

⇒ $5035 = P (1 + ²/₁₀₀ × 3)

⇒ $5035 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $5035 = P (1 + ⁶/₁₀₀)

⇒ $5035 = P (^{100 + 6}/₁₀₀)

⇒ $5035 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $5035

⇒ P = ⁵⁰³⁵/_¹⁰⁶/100

⇒ P = 5035 × ¹⁰⁰/₁₀₆

⇒ P = ^{5035 × 100}/₁₀₆

⇒ P = ⁵⁰³⁵⁰⁰/₁₀₆

⇒ P = $4750

Thus, the sum borrowed (P) = $4750 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 5035, then the Principal = ¹⁰⁰/₁₀₆ × 5035

= ^{100 × 5035}/₁₀₆

= ⁵⁰³⁵⁰⁰/₁₀₆

= 4750

Thus, Principal = $4750

Thus, the sum borrowed = $4750 Answer

Similar Questions

(1) How much loan did Michael borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6095 to clear it?

(2) If David paid $4080 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.

(4) If Patricia paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) How much loan did Sharon borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8525 to clear it?

(6) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.

(7) In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?

(8) How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?

(9) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 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 $10880 to clear the loan, then find the time period of the loan.