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) If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 7 years.

(3) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 7% simple interest?

(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 8 years.

(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 3 years.

(6) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 8% simple interest?

(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 8 years.

(8) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 3 years.

(9) If Elizabeth borrowed $3450 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(10) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.