Simple Interest
Math MCQs

Question :    How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?

Correct Answer  $7400

Solution & Explanation

Solution

Given,

Amount (A) = $9250

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

$9250 = P (1 + 5% × 5)

⇒ $9250 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9250 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9250 = P (1 + ²⁵/₁₀₀)

⇒ $9250 = P (^{100 + 25}/₁₀₀)

⇒ $9250 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9250

⇒ P = ⁹²⁵⁰/_¹²⁵/100

⇒ P = 9250 × ¹⁰⁰/₁₂₅

⇒ P = ^{9250 × 100}/₁₂₅

⇒ P = ⁹²⁵⁰⁰⁰/₁₂₅

⇒ P = $7400

Thus, the sum borrowed (P) = $7400 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 9250, then the Principal = ¹⁰⁰/₁₂₅ × 9250

= ^{100 × 9250}/₁₂₅

= ⁹²⁵⁰⁰⁰/₁₂₅

= 7400

Thus, Principal = $7400

Thus, the sum borrowed = $7400 Answer

Similar Questions

(1) If Betty paid $5100 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.

(3) 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?

(4) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.

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

(6) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 7 years.

(8) If Charles paid $4212 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 2% simple interest.

(10) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.