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) How much loan did James borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6250 to clear it?

(2) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 10% simple interest?

(3) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 3 years.

(4) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.

(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.

(6) How much loan did Lisa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7260 to clear it?

(7) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 8 years.

(8) In how much time a principal of $3000 will amount to $3300 at a simple interest of 5% per annum?

(9) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?

(10) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?