Simple Interest
Math MCQs

Question :    How much loan did Rebecca borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9562.5 to clear it?

Correct Answer  $7650

Solution & Explanation

Solution

Given,

Amount (A) = $9562.5

Rate of Simple Interest (R) = 5%

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

$9562.5 = P (1 + 5% × 5)

⇒ $9562.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9562.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9562.5 = P (1 + ²⁵/₁₀₀)

⇒ $9562.5 = P (^{100 + 25}/₁₀₀)

⇒ $9562.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9562.5

⇒ P = ^9562.5/_¹²⁵/100

⇒ P = 9562.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{9562.5 × 100}/₁₂₅

⇒ P = ⁹⁵⁶²⁵⁰/₁₂₅

⇒ 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 9562.5, then the Principal = ¹⁰⁰/₁₂₅ × 9562.5

= ^{100 × 9562.5}/₁₂₅

= ⁹⁵⁶²⁵⁰/₁₂₅

= 7650

Thus, Principal = $7650

Thus, the sum borrowed = $7650 Answer

Similar Questions

(1) In how much time a principal of $3100 will amount to $3348 at a simple interest of 2% per annum?

(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.

(3) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.

(4) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 9% simple interest.

(5) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 2% simple interest.

(6) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 8 years.

(7) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 9% simple interest?

(8) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 4 years.

(9) How much loan did George borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8760 to clear it?

(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 7 years.