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) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?

(2) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 7 years.

(3) How much loan did Ashley borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7205 to clear it?

(4) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.

(5) Jennifer had to pay $3737.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) In how much time a principal of $3050 will amount to $3812.5 at a simple interest of 5% per annum?

(7) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9360 to clear it?

(8) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.

(9) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $5848 to clear the loan, then find the time period of the loan.

(10) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?