Simple Interest
Math MCQs

Question :  ( 8 of 10 )  How much loan did Edward borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8360 to clear it?

Correct Answer  $7600

Solution & Explanation

Solution

Given,

Amount (A) = $8360

Rate of Simple Interest (R) = 2%

Time (T) = 5 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

$8360 = P (1 + 2% × 5)

⇒ $8360 = P (1 + ²/₁₀₀ × 5)

⇒ $8360 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8360 = P (1 + ¹⁰/₁₀₀)

⇒ $8360 = P (^{100 + 10}/₁₀₀)

⇒ $8360 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8360

⇒ P = ⁸³⁶⁰/_¹¹⁰/100

⇒ P = 8360 × ¹⁰⁰/₁₁₀

⇒ P = ^{8360 × 100}/₁₁₀

⇒ P = ⁸³⁶⁰⁰⁰/₁₁₀

⇒ P = $7600

Thus, the sum borrowed (P) = $7600 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 = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 8360, then the Principal = ¹⁰⁰/₁₁₀ × 8360

= ^{100 × 8360}/₁₁₀

= ⁸³⁶⁰⁰⁰/₁₁₀

= 7600

Thus, Principal = $7600

Thus, the sum borrowed = $7600 Answer

Similar Questions

(1) How much loan did Robert borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6120 to clear it?

(2) Michelle had to pay $5247 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 10% simple interest?

(4) How much loan did Charles borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6785 to clear it?

(5) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.

(6) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.

(7) If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(8) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 7 years.

(9) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.

(10) 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.