Simple Interest
Math MCQs

Question :    How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?

Correct Answer  $7450

Solution & Explanation

Solution

Given,

Amount (A) = $9312.5

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

$9312.5 = P (1 + 5% × 5)

⇒ $9312.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9312.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9312.5 = P (1 + ²⁵/₁₀₀)

⇒ $9312.5 = P (^{100 + 25}/₁₀₀)

⇒ $9312.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9312.5

⇒ P = ^9312.5/_¹²⁵/100

⇒ P = 9312.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{9312.5 × 100}/₁₂₅

⇒ P = ⁹³¹²⁵⁰/₁₂₅

⇒ P = $7450

Thus, the sum borrowed (P) = $7450 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 9312.5, then the Principal = ¹⁰⁰/₁₂₅ × 9312.5

= ^{100 × 9312.5}/₁₂₅

= ⁹³¹²⁵⁰/₁₂₅

= 7450

Thus, Principal = $7450

Thus, the sum borrowed = $7450 Answer

Similar Questions

(1) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7599 to clear the loan, then find the time period of the loan.

(2) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 6% simple interest?

(3) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 9% simple interest?

(4) What amount does David have to pay after 5 years if he takes a loan of $3400 at 10% simple interest?

(5) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.

(6) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.

(7) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(8) How much loan did Daniel borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6710 to clear it?

(9) If Anthony paid $4988 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(10) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.