Simple Interest
Math MCQs

Question :    How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?

Correct Answer  $6250

Solution & Explanation

Solution

Given,

Amount (A) = $6875

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

$6875 = P (1 + 2% × 5)

⇒ $6875 = P (1 + ²/₁₀₀ × 5)

⇒ $6875 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6875 = P (1 + ¹⁰/₁₀₀)

⇒ $6875 = P (^{100 + 10}/₁₀₀)

⇒ $6875 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6875

⇒ P = ⁶⁸⁷⁵/_¹¹⁰/100

⇒ P = 6875 × ¹⁰⁰/₁₁₀

⇒ P = ^{6875 × 100}/₁₁₀

⇒ P = ⁶⁸⁷⁵⁰⁰/₁₁₀

⇒ P = $6250

Thus, the sum borrowed (P) = $6250 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 6875, then the Principal = ¹⁰⁰/₁₁₀ × 6875

= ^{100 × 6875}/₁₁₀

= ⁶⁸⁷⁵⁰⁰/₁₁₀

= 6250

Thus, Principal = $6250

Thus, the sum borrowed = $6250 Answer

Similar Questions

(1) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 4 years.

(3) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.

(4) What amount does James have to pay after 6 years if he takes a loan of $3000 at 10% simple interest?

(5) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.

(6) How much loan did Barbara borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6660 to clear it?

(7) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 4 years.

(8) If Joseph paid $4292 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(9) If Mary paid $3660 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 4 years.