Simple Interest
Math MCQs

Question :    How much loan did Jacob borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9600 to clear it?

Correct Answer  $8000

Solution & Explanation

Solution

Given,

Amount (A) = $9600

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

$9600 = P (1 + 4% × 5)

⇒ $9600 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9600 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9600 = P (1 + ²⁰/₁₀₀)

⇒ $9600 = P (^{100 + 20}/₁₀₀)

⇒ $9600 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9600

⇒ P = ⁹⁶⁰⁰/_¹²⁰/100

⇒ P = 9600 × ¹⁰⁰/₁₂₀

⇒ P = ^{9600 × 100}/₁₂₀

⇒ P = ⁹⁶⁰⁰⁰⁰/₁₂₀

⇒ P = $8000

Thus, the sum borrowed (P) = $8000 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 9600, then the Principal = ¹⁰⁰/₁₂₀ × 9600

= ^{100 × 9600}/₁₂₀

= ⁹⁶⁰⁰⁰⁰/₁₂₀

= 8000

Thus, Principal = $8000

Thus, the sum borrowed = $8000 Answer

Similar Questions

(1) Steven had to pay $5290 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9676 to clear the loan, then find the time period of the loan.

(3) 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.

(4) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.

(5) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 9% simple interest?

(6) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 4 years.

(7) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.

(8) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.

(10) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 9% simple interest.