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) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 4 years.

(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 3 years.

(3) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8580 to clear it?

(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.

(5) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.

(6) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 8% simple interest?

(7) How much loan did Steven borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8250 to clear it?

(8) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 8% simple interest?

(9) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 7 years.

(10) In how much time a principal of $3200 will amount to $3392 at a simple interest of 3% per annum?