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) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 4 years.

(2) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(3) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 5% simple interest?

(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 7 years.

(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 3 years.

(6) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7748 to clear the loan, then find the time period of the loan.

(7) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.

(8) If Barbara paid $4260 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.

(10) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $6936 to clear the loan, then find the time period of the loan.