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) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.

(2) What amount does John have to pay after 5 years if he takes a loan of $3200 at 10% simple interest?

(3) In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?

(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 8 years.

(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 4 years.

(6) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.

(8) If Mary paid $3538 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(9) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.

(10) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $10498 to clear the loan, then find the time period of the loan.