Simple Interest
Math MCQs

Question :    How much loan did Sharon borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8525 to clear it?

Correct Answer  $7750

Solution & Explanation

Solution

Given,

Amount (A) = $8525

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

$8525 = P (1 + 2% × 5)

⇒ $8525 = P (1 + ²/₁₀₀ × 5)

⇒ $8525 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8525 = P (1 + ¹⁰/₁₀₀)

⇒ $8525 = P (^{100 + 10}/₁₀₀)

⇒ $8525 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8525

⇒ P = ⁸⁵²⁵/_¹¹⁰/100

⇒ P = 8525 × ¹⁰⁰/₁₁₀

⇒ P = ^{8525 × 100}/₁₁₀

⇒ P = ⁸⁵²⁵⁰⁰/₁₁₀

⇒ P = $7750

Thus, the sum borrowed (P) = $7750 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 8525, then the Principal = ¹⁰⁰/₁₁₀ × 8525

= ^{100 × 8525}/₁₁₀

= ⁸⁵²⁵⁰⁰/₁₁₀

= 7750

Thus, Principal = $7750

Thus, the sum borrowed = $7750 Answer

Similar Questions

(1) 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?

(2) In how much time a principal of $3200 will amount to $4000 at a simple interest of 5% per annum?

(3) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 3 years.

(4) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 2% simple interest.

(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.

(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 3 years.

(7) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6407 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 3 years.

(9) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10136 to clear the loan, then find the time period of the loan.

(10) How much loan did Mary borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6312.5 to clear it?