Simple Interest
Math MCQs

Question :  ( 1 of 10 )  How much loan did Melissa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8085 to clear it?

Correct Answer  $7350

Solution & Explanation

Solution

Given,

Amount (A) = $8085

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

$8085 = P (1 + 2% × 5)

⇒ $8085 = P (1 + ²/₁₀₀ × 5)

⇒ $8085 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8085 = P (1 + ¹⁰/₁₀₀)

⇒ $8085 = P (^{100 + 10}/₁₀₀)

⇒ $8085 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8085

⇒ P = ⁸⁰⁸⁵/_¹¹⁰/100

⇒ P = 8085 × ¹⁰⁰/₁₁₀

⇒ P = ^{8085 × 100}/₁₁₀

⇒ P = ⁸⁰⁸⁵⁰⁰/₁₁₀

⇒ P = $7350

Thus, the sum borrowed (P) = $7350 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 8085, then the Principal = ¹⁰⁰/₁₁₀ × 8085

= ^{100 × 8085}/₁₁₀

= ⁸⁰⁸⁵⁰⁰/₁₁₀

= 7350

Thus, Principal = $7350

Thus, the sum borrowed = $7350 Answer

Similar Questions

(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.

(2) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.

(3) How much loan did Matthew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7130 to clear it?

(4) Kenneth had to pay $5750 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(5) What amount does John have to pay after 6 years if he takes a loan of $3200 at 3% simple interest?

(6) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7072 to clear the loan, then find the time period of the loan.

(7) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 5% simple interest?

(8) If Sarah paid $4158 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6300 to clear it?

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