Simple Interest
Math MCQs

Question :    How much loan did Rebecca borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8797.5 to clear it?

Correct Answer  $7650

Solution & Explanation

Solution

Given,

Amount (A) = $8797.5

Rate of Simple Interest (R) = 3%

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

$8797.5 = P (1 + 3% × 5)

⇒ $8797.5 = P (1 + ³/₁₀₀ × 5)

⇒ $8797.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8797.5 = P (1 + ¹⁵/₁₀₀)

⇒ $8797.5 = P (^{100 + 15}/₁₀₀)

⇒ $8797.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8797.5

⇒ P = ^8797.5/_¹¹⁵/100

⇒ P = 8797.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{8797.5 × 100}/₁₁₅

⇒ P = ⁸⁷⁹⁷⁵⁰/₁₁₅

⇒ P = $7650

Thus, the sum borrowed (P) = $7650 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 8797.5, then the Principal = ¹⁰⁰/₁₁₅ × 8797.5

= ^{100 × 8797.5}/₁₁₅

= ⁸⁷⁹⁷⁵⁰/₁₁₅

= 7650

Thus, Principal = $7650

Thus, the sum borrowed = $7650 Answer

Similar Questions

(1) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.

(2) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 3 years.

(4) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.

(5) If Ashley paid $5460 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) What amount does David have to pay after 5 years if he takes a loan of $3400 at 7% simple interest?

(7) What amount does David have to pay after 5 years if he takes a loan of $3400 at 9% simple interest?

(8) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.

(10) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.