Simple Interest
Math MCQs

Question :    How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?

Correct Answer  $7850

Solution & Explanation

Solution

Given,

Amount (A) = $8635

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

$8635 = P (1 + 2% × 5)

⇒ $8635 = P (1 + ²/₁₀₀ × 5)

⇒ $8635 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8635 = P (1 + ¹⁰/₁₀₀)

⇒ $8635 = P (^{100 + 10}/₁₀₀)

⇒ $8635 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8635

⇒ P = ⁸⁶³⁵/_¹¹⁰/100

⇒ P = 8635 × ¹⁰⁰/₁₁₀

⇒ P = ^{8635 × 100}/₁₁₀

⇒ P = ⁸⁶³⁵⁰⁰/₁₁₀

⇒ P = $7850

Thus, the sum borrowed (P) = $7850 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 8635, then the Principal = ¹⁰⁰/₁₁₀ × 8635

= ^{100 × 8635}/₁₁₀

= ⁸⁶³⁵⁰⁰/₁₁₀

= 7850

Thus, Principal = $7850

Thus, the sum borrowed = $7850 Answer

Similar Questions

(1) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5960 to clear the loan, then find the time period of the loan.

(2) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9020 to clear the loan, then find the time period of the loan.

(3) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.

(4) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 5% simple interest?

(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 7 years.

(6) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 7 years.

(8) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 10% simple interest?

(9) If William paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 8 years.