Simple Interest
Math MCQs

Question :    How much loan did Lisa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6655 to clear it?

Correct Answer  $6050

Solution & Explanation

Solution

Given,

Amount (A) = $6655

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

$6655 = P (1 + 2% × 5)

⇒ $6655 = P (1 + ²/₁₀₀ × 5)

⇒ $6655 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6655 = P (1 + ¹⁰/₁₀₀)

⇒ $6655 = P (^{100 + 10}/₁₀₀)

⇒ $6655 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6655

⇒ P = ⁶⁶⁵⁵/_¹¹⁰/100

⇒ P = 6655 × ¹⁰⁰/₁₁₀

⇒ P = ^{6655 × 100}/₁₁₀

⇒ P = ⁶⁶⁵⁵⁰⁰/₁₁₀

⇒ P = $6050

Thus, the sum borrowed (P) = $6050 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 6655, then the Principal = ¹⁰⁰/₁₁₀ × 6655

= ^{100 × 6655}/₁₁₀

= ⁶⁶⁵⁵⁰⁰/₁₁₀

= 6050

Thus, Principal = $6050

Thus, the sum borrowed = $6050 Answer

Similar Questions

(1) In how much time a principal of $3000 will amount to $3450 at a simple interest of 3% per annum?

(2) How much loan did Mark borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7360 to clear it?

(3) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.

(4) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 8 years.

(6) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.

(7) How much loan did Linda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6152.5 to clear it?

(8) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.

(9) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $11480 to clear the loan, then find the time period of the loan.

(10) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 9% simple interest?