Simple Interest
Math MCQs

Question :    How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?

Correct Answer  $7050

Solution & Explanation

Solution

Given,

Amount (A) = $7755

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

$7755 = P (1 + 2% × 5)

⇒ $7755 = P (1 + ²/₁₀₀ × 5)

⇒ $7755 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7755 = P (1 + ¹⁰/₁₀₀)

⇒ $7755 = P (^{100 + 10}/₁₀₀)

⇒ $7755 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7755

⇒ P = ⁷⁷⁵⁵/_¹¹⁰/100

⇒ P = 7755 × ¹⁰⁰/₁₁₀

⇒ P = ^{7755 × 100}/₁₁₀

⇒ P = ⁷⁷⁵⁵⁰⁰/₁₁₀

⇒ P = $7050

Thus, the sum borrowed (P) = $7050 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 7755, then the Principal = ¹⁰⁰/₁₁₀ × 7755

= ^{100 × 7755}/₁₁₀

= ⁷⁷⁵⁵⁰⁰/₁₁₀

= 7050

Thus, Principal = $7050

Thus, the sum borrowed = $7050 Answer

Similar Questions

(1) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 7% simple interest?

(2) Patricia had to pay $3622.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 8% simple interest?

(5) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 10% simple interest?

(6) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.

(7) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.

(8) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?

(9) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 3% simple interest.