Simple Interest
Math MCQs

Question :    How much loan did Lisa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7562.5 to clear it?

Correct Answer  $6050

Solution & Explanation

Solution

Given,

Amount (A) = $7562.5

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

$7562.5 = P (1 + 5% × 5)

⇒ $7562.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7562.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7562.5 = P (1 + ²⁵/₁₀₀)

⇒ $7562.5 = P (^{100 + 25}/₁₀₀)

⇒ $7562.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7562.5

⇒ P = ^7562.5/_¹²⁵/100

⇒ P = 7562.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{7562.5 × 100}/₁₂₅

⇒ P = ⁷⁵⁶²⁵⁰/₁₂₅

⇒ P = $6050

Thus, the sum borrowed (P) = $6050 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 7562.5, then the Principal = ¹⁰⁰/₁₂₅ × 7562.5

= ^{100 × 7562.5}/₁₂₅

= ⁷⁵⁶²⁵⁰/₁₂₅

= 6050

Thus, Principal = $6050

Thus, the sum borrowed = $6050 Answer

Similar Questions

(1) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?

(2) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.

(3) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 4% simple interest.

(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 8 years.

(5) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 8 years.

(6) How much loan did Matthew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7750 to clear it?

(7) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 2% simple interest?

(8) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.

(9) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 8% simple interest?

(10) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 7 years.