Simple Interest
Math MCQs

Question :    How much loan did Sandra borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7095 to clear it?

Correct Answer  $6450

Solution & Explanation

Solution

Given,

Amount (A) = $7095

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

$7095 = P (1 + 2% × 5)

⇒ $7095 = P (1 + ²/₁₀₀ × 5)

⇒ $7095 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7095 = P (1 + ¹⁰/₁₀₀)

⇒ $7095 = P (^{100 + 10}/₁₀₀)

⇒ $7095 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7095

⇒ P = ⁷⁰⁹⁵/_¹¹⁰/100

⇒ P = 7095 × ¹⁰⁰/₁₁₀

⇒ P = ^{7095 × 100}/₁₁₀

⇒ P = ⁷⁰⁹⁵⁰⁰/₁₁₀

⇒ P = $6450

Thus, the sum borrowed (P) = $6450 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 7095, then the Principal = ¹⁰⁰/₁₁₀ × 7095

= ^{100 × 7095}/₁₁₀

= ⁷⁰⁹⁵⁰⁰/₁₁₀

= 6450

Thus, Principal = $6450

Thus, the sum borrowed = $6450 Answer

Similar Questions

(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 8 years.

(2) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.

(3) How much loan did Sharon borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9687.5 to clear it?

(4) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 8 years.

(5) How much loan did Jacob borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8800 to clear it?

(6) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.

(7) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 7% simple interest?

(8) How much loan did David borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5940 to clear it?

(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 4 years.

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