Simple Interest
Math MCQs

Question :    How much loan did Emily borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8100 to clear it?

Correct Answer  $6750

Solution & Explanation

Solution

Given,

Amount (A) = $8100

Rate of Simple Interest (R) = 4%

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

$8100 = P (1 + 4% × 5)

⇒ $8100 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8100 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8100 = P (1 + ²⁰/₁₀₀)

⇒ $8100 = P (^{100 + 20}/₁₀₀)

⇒ $8100 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8100

⇒ P = ⁸¹⁰⁰/_¹²⁰/100

⇒ P = 8100 × ¹⁰⁰/₁₂₀

⇒ P = ^{8100 × 100}/₁₂₀

⇒ P = ⁸¹⁰⁰⁰⁰/₁₂₀

⇒ P = $6750

Thus, the sum borrowed (P) = $6750 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 8100, then the Principal = ¹⁰⁰/₁₂₀ × 8100

= ^{100 × 8100}/₁₂₀

= ⁸¹⁰⁰⁰⁰/₁₂₀

= 6750

Thus, Principal = $6750

Thus, the sum borrowed = $6750 Answer

Similar Questions

(1) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.

(2) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 4 years.

(4) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 4% simple interest?

(5) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.

(6) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5576 to clear the loan, then find the time period of the loan.

(7) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) In how much time a principal of $3150 will amount to $3780 at a simple interest of 4% per annum?

(9) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.

(10) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.