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) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.

(2) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.

(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 7% simple interest?

(4) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.

(5) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 8% simple interest?

(6) If Matthew paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.

(8) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.

(9) How much loan did Susan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7062.5 to clear it?

(10) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.