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) In how much time a principal of $3000 will amount to $3450 at a simple interest of 3% per annum?

(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.

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

(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 3 years.

(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 7 years.

(6) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.

(7) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.

(8) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 4% simple interest?

(9) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 3% simple interest?

(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 8 years.