Simple Interest
Math MCQs

Question :    How much loan did Brian borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9000 to clear it?

Correct Answer  $7200

Solution & Explanation

Solution

Given,

Amount (A) = $9000

Rate of Simple Interest (R) = 5%

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

$9000 = P (1 + 5% × 5)

⇒ $9000 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9000 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9000 = P (1 + ²⁵/₁₀₀)

⇒ $9000 = P (^{100 + 25}/₁₀₀)

⇒ $9000 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9000

⇒ P = ⁹⁰⁰⁰/_¹²⁵/100

⇒ P = 9000 × ¹⁰⁰/₁₂₅

⇒ P = ^{9000 × 100}/₁₂₅

⇒ P = ⁹⁰⁰⁰⁰⁰/₁₂₅

⇒ P = $7200

Thus, the sum borrowed (P) = $7200 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 9000, then the Principal = ¹⁰⁰/₁₂₅ × 9000

= ^{100 × 9000}/₁₂₅

= ⁹⁰⁰⁰⁰⁰/₁₂₅

= 7200

Thus, Principal = $7200

Thus, the sum borrowed = $7200 Answer

Similar Questions

(1) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?

(2) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.

(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.

(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 3 years.

(5) If Patricia paid $3402 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) If Sarah borrowed $3850 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(7) How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?

(8) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.

(10) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 3% simple interest?