Simple Interest
Math MCQs

Question :    How much loan did Joseph borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6270 to clear it?

Correct Answer  $5700

Solution & Explanation

Solution

Given,

Amount (A) = $6270

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

$6270 = P (1 + 2% × 5)

⇒ $6270 = P (1 + ²/₁₀₀ × 5)

⇒ $6270 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6270 = P (1 + ¹⁰/₁₀₀)

⇒ $6270 = P (^{100 + 10}/₁₀₀)

⇒ $6270 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6270

⇒ P = ⁶²⁷⁰/_¹¹⁰/100

⇒ P = 6270 × ¹⁰⁰/₁₁₀

⇒ P = ^{6270 × 100}/₁₁₀

⇒ P = ⁶²⁷⁰⁰⁰/₁₁₀

⇒ P = $5700

Thus, the sum borrowed (P) = $5700 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 6270, then the Principal = ¹⁰⁰/₁₁₀ × 6270

= ^{100 × 6270}/₁₁₀

= ⁶²⁷⁰⁰⁰/₁₁₀

= 5700

Thus, Principal = $5700

Thus, the sum borrowed = $5700 Answer

Similar Questions

(1) If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 10% simple interest?

(3) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.

(4) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.

(5) If Joseph borrowed $3700 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(6) In how much time a principal of $3000 will amount to $3360 at a simple interest of 4% per annum?

(7) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?

(8) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 7% simple interest?

(9) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 5% simple interest for 3 years.