Simple Interest
Math MCQs

Question :    How much loan did Margaret borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6985 to clear it?

Correct Answer  $6350

Solution & Explanation

Solution

Given,

Amount (A) = $6985

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

$6985 = P (1 + 2% × 5)

⇒ $6985 = P (1 + ²/₁₀₀ × 5)

⇒ $6985 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6985 = P (1 + ¹⁰/₁₀₀)

⇒ $6985 = P (^{100 + 10}/₁₀₀)

⇒ $6985 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6985

⇒ P = ⁶⁹⁸⁵/_¹¹⁰/100

⇒ P = 6985 × ¹⁰⁰/₁₁₀

⇒ P = ^{6985 × 100}/₁₁₀

⇒ P = ⁶⁹⁸⁵⁰⁰/₁₁₀

⇒ P = $6350

Thus, the sum borrowed (P) = $6350 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 6985, then the Principal = ¹⁰⁰/₁₁₀ × 6985

= ^{100 × 6985}/₁₁₀

= ⁶⁹⁸⁵⁰⁰/₁₁₀

= 6350

Thus, Principal = $6350

Thus, the sum borrowed = $6350 Answer

Similar Questions

(1) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 8 years.

(3) If Matthew paid $4704 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 7 years.

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

(6) In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum?

(7) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 7 years.

(9) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 4 years.

(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 8 years.