Simple Interest
Math MCQs

Question :    How much loan did Rebecca borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9180 to clear it?

Correct Answer  $7650

Solution & Explanation

Solution

Given,

Amount (A) = $9180

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

$9180 = P (1 + 4% × 5)

⇒ $9180 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9180 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9180 = P (1 + ²⁰/₁₀₀)

⇒ $9180 = P (^{100 + 20}/₁₀₀)

⇒ $9180 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9180

⇒ P = ⁹¹⁸⁰/_¹²⁰/100

⇒ P = 9180 × ¹⁰⁰/₁₂₀

⇒ P = ^{9180 × 100}/₁₂₀

⇒ P = ⁹¹⁸⁰⁰⁰/₁₂₀

⇒ P = $7650

Thus, the sum borrowed (P) = $7650 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 9180, then the Principal = ¹⁰⁰/₁₂₀ × 9180

= ^{100 × 9180}/₁₂₀

= ⁹¹⁸⁰⁰⁰/₁₂₀

= 7650

Thus, Principal = $7650

Thus, the sum borrowed = $7650 Answer

Similar Questions

(1) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 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 8% simple interest for 4 years.

(3) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.

(4) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.

(5) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.

(6) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.

(7) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 7% simple interest?

(9) Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.