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) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 7 years.

(2) If Thomas paid $4104 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) If Donna paid $5820 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(4) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 5% simple interest.

(5) How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?

(6) If Patricia borrowed $3150 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(7) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 8 years.

(9) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?

(10) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8507 to clear the loan, then find the time period of the loan.