Simple Interest
Math MCQs

Question :    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?

Correct Answer  $6800

Solution & Explanation

Solution

Given,

Amount (A) = $7480

Rate of Simple Interest (R) = 2%

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

$7480 = P (1 + 2% × 5)

⇒ $7480 = P (1 + ²/₁₀₀ × 5)

⇒ $7480 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7480 = P (1 + ¹⁰/₁₀₀)

⇒ $7480 = P (^{100 + 10}/₁₀₀)

⇒ $7480 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7480

⇒ P = ⁷⁴⁸⁰/_¹¹⁰/100

⇒ P = 7480 × ¹⁰⁰/₁₁₀

⇒ P = ^{7480 × 100}/₁₁₀

⇒ P = ⁷⁴⁸⁰⁰⁰/₁₁₀

⇒ 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 7480, then the Principal = ¹⁰⁰/₁₁₀ × 7480

= ^{100 × 7480}/₁₁₀

= ⁷⁴⁸⁰⁰⁰/₁₁₀

= 6800

Thus, Principal = $6800

Thus, the sum borrowed = $6800 Answer

Similar Questions

(1) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.

(2) 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?

(3) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 5% simple interest?

(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 3 years.

(5) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.

(6) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 3 years.

(7) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.

(8) If Donald paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) If Barbara paid $4118 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 5% simple interest?