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 Patricia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6437.5 to clear it?

(2) What amount does John have to pay after 5 years if he takes a loan of $3200 at 3% simple interest?

(3) How much loan did Sandra borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7740 to clear it?

(4) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.

(5) If Nancy paid $4482 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) If Paul paid $5640 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 10% simple interest?

(8) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.

(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 8 years.

(10) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.