Simple Interest
Math MCQs

Question :    How much loan did Nancy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7072.5 to clear it?

Correct Answer  $6150

Solution & Explanation

Solution

Given,

Amount (A) = $7072.5

Rate of Simple Interest (R) = 3%

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

$7072.5 = P (1 + 3% × 5)

⇒ $7072.5 = P (1 + ³/₁₀₀ × 5)

⇒ $7072.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7072.5 = P (1 + ¹⁵/₁₀₀)

⇒ $7072.5 = P (^{100 + 15}/₁₀₀)

⇒ $7072.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7072.5

⇒ P = ^7072.5/_¹¹⁵/100

⇒ P = 7072.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{7072.5 × 100}/₁₁₅

⇒ P = ⁷⁰⁷²⁵⁰/₁₁₅

⇒ P = $6150

Thus, the sum borrowed (P) = $6150 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 7072.5, then the Principal = ¹⁰⁰/₁₁₅ × 7072.5

= ^{100 × 7072.5}/₁₁₅

= ⁷⁰⁷²⁵⁰/₁₁₅

= 6150

Thus, Principal = $6150

Thus, the sum borrowed = $6150 Answer

Similar Questions

(1) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.

(3) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?

(4) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10860 to clear the loan, then find the time period of the loan.

(5) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 8 years.

(7) How much loan did Betty borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7500 to clear it?

(8) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 5% simple interest?

(9) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 3 years.