Simple Interest
Math MCQs

Question :    How much loan did Kevin borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7810 to clear it?

Correct Answer  $7100

Solution & Explanation

Solution

Given,

Amount (A) = $7810

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

$7810 = P (1 + 2% × 5)

⇒ $7810 = P (1 + ²/₁₀₀ × 5)

⇒ $7810 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7810 = P (1 + ¹⁰/₁₀₀)

⇒ $7810 = P (^{100 + 10}/₁₀₀)

⇒ $7810 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7810

⇒ P = ⁷⁸¹⁰/_¹¹⁰/100

⇒ P = 7810 × ¹⁰⁰/₁₁₀

⇒ P = ^{7810 × 100}/₁₁₀

⇒ P = ⁷⁸¹⁰⁰⁰/₁₁₀

⇒ P = $7100

Thus, the sum borrowed (P) = $7100 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 7810, then the Principal = ¹⁰⁰/₁₁₀ × 7810

= ^{100 × 7810}/₁₁₀

= ⁷⁸¹⁰⁰⁰/₁₁₀

= 7100

Thus, Principal = $7100

Thus, the sum borrowed = $7100 Answer

Similar Questions

(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.

(2) If Susan borrowed $3650 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(3) In how much time a principal of $3100 will amount to $3565 at a simple interest of 3% per annum?

(4) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9536 to clear the loan, then find the time period of the loan.

(5) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11041 to clear the loan, then find the time period of the loan.

(6) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

(7) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.

(8) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 9% simple interest?

(9) What amount does William have to pay after 6 years if he takes a loan of $3500 at 7% simple interest?

(10) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.