Simple Interest
Math MCQs

Question :    Nancy had to pay $4772.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

Correct Answer  $4150

Solution & Explanation

Solution

Given,

Amount (A) = $4772.5

Rate of Simple Interest (R) = 5%

Time (T) = 3 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

$4772.5 = P (1 + 5% × 3)

⇒ $4772.5 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4772.5 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4772.5 = P (1 + ¹⁵/₁₀₀)

⇒ $4772.5 = P (^{100 + 15}/₁₀₀)

⇒ $4772.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4772.5

⇒ P = ^4772.5/_¹¹⁵/100

⇒ P = 4772.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{4772.5 × 100}/₁₁₅

⇒ P = ⁴⁷⁷²⁵⁰/₁₁₅

⇒ P = $4150

Thus, the sum borrowed (P) = $4150 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 5 = 15

Thus, simple interest for 3 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 4772.5, then the Principal = ¹⁰⁰/₁₁₅ × 4772.5

= ^{100 × 4772.5}/₁₁₅

= ⁴⁷⁷²⁵⁰/₁₁₅

= 4150

Thus, Principal = $4150

Thus, the sum borrowed = $4150 Answer

Similar Questions

(1) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 3 years.

(2) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.

(3) If Joshua paid $5880 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(4) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 4 years.

(5) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 8 years.

(6) James had to pay $3180 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.

(8) How much loan did Edward borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9500 to clear it?

(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 7 years.

(10) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.