Simple Interest
Math MCQs

Question :    How much loan did Edward borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9120 to clear it?

Correct Answer  $7600

Solution & Explanation

Solution

Given,

Amount (A) = $9120

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

$9120 = P (1 + 4% × 5)

⇒ $9120 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9120 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9120 = P (1 + ²⁰/₁₀₀)

⇒ $9120 = P (^{100 + 20}/₁₀₀)

⇒ $9120 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9120

⇒ P = ⁹¹²⁰/_¹²⁰/100

⇒ P = 9120 × ¹⁰⁰/₁₂₀

⇒ P = ^{9120 × 100}/₁₂₀

⇒ P = ⁹¹²⁰⁰⁰/₁₂₀

⇒ 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 = 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 9120, then the Principal = ¹⁰⁰/₁₂₀ × 9120

= ^{100 × 9120}/₁₂₀

= ⁹¹²⁰⁰⁰/₁₂₀

= 7600

Thus, Principal = $7600

Thus, the sum borrowed = $7600 Answer

Similar Questions

(1) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 3 years.

(3) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.

(4) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?

(5) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11946 to clear the loan, then find the time period of the loan.

(6) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.

(7) David had to pay $3604 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 4 years.

(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 8 years.

(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 8 years.