Simple Interest
Math MCQs

Question :    How much loan did Andrew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7820 to clear it?

Correct Answer  $6800

Solution & Explanation

Solution

Given,

Amount (A) = $7820

Rate of Simple Interest (R) = 3%

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

$7820 = P (1 + 3% × 5)

⇒ $7820 = P (1 + ³/₁₀₀ × 5)

⇒ $7820 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7820 = P (1 + ¹⁵/₁₀₀)

⇒ $7820 = P (^{100 + 15}/₁₀₀)

⇒ $7820 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7820

⇒ P = ⁷⁸²⁰/_¹¹⁵/100

⇒ P = 7820 × ¹⁰⁰/₁₁₅

⇒ P = ^{7820 × 100}/₁₁₅

⇒ P = ⁷⁸²⁰⁰⁰/₁₁₅

⇒ P = $6800

Thus, the sum borrowed (P) = $6800 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 7820, then the Principal = ¹⁰⁰/₁₁₅ × 7820

= ^{100 × 7820}/₁₁₅

= ⁷⁸²⁰⁰⁰/₁₁₅

= 6800

Thus, Principal = $6800

Thus, the sum borrowed = $6800 Answer

Similar Questions

(1) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 7 years.

(2) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.

(3) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Charles borrowed a sum of $3900 at 4% simple interest for 3 years.

(5) If Joseph paid $4292 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.

(7) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.

(8) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.

(10) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 7% simple interest.