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) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 5% simple interest?

(2) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.

(4) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 4% simple interest.

(5) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 4 years.

(6) How much loan did Michelle borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8687.5 to clear it?

(7) If Matthew paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 7 years.

(9) If Jessica paid $4500 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Richard had to pay $3816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.