Simple Interest
Math MCQs

Question :    How much loan did James borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6000 to clear it?

Correct Answer  $5000

Solution & Explanation

Solution

Given,

Amount (A) = $6000

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

$6000 = P (1 + 4% × 5)

⇒ $6000 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6000 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6000 = P (1 + ²⁰/₁₀₀)

⇒ $6000 = P (^{100 + 20}/₁₀₀)

⇒ $6000 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6000

⇒ P = ⁶⁰⁰⁰/_¹²⁰/100

⇒ P = 6000 × ¹⁰⁰/₁₂₀

⇒ P = ^{6000 × 100}/₁₂₀

⇒ P = ⁶⁰⁰⁰⁰⁰/₁₂₀

⇒ P = $5000

Thus, the sum borrowed (P) = $5000 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 6000, then the Principal = ¹⁰⁰/₁₂₀ × 6000

= ^{100 × 6000}/₁₂₀

= ⁶⁰⁰⁰⁰⁰/₁₂₀

= 5000

Thus, Principal = $5000

Thus, the sum borrowed = $5000 Answer

Similar Questions

(1) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.

(2) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.

(3) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.

(4) 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.

(5) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 5% simple interest?

(6) If Charles paid $4524 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 8 years.

(9) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7599 to clear the loan, then find the time period of the loan.

(10) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 8% simple interest?