Simple Interest
Math MCQs

Question :    Charles had to pay $4485 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  $3900

Solution & Explanation

Solution

Given,

Amount (A) = $4485

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

$4485 = P (1 + 5% × 3)

⇒ $4485 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4485 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4485 = P (1 + ¹⁵/₁₀₀)

⇒ $4485 = P (^{100 + 15}/₁₀₀)

⇒ $4485 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4485

⇒ P = ⁴⁴⁸⁵/_¹¹⁵/100

⇒ P = 4485 × ¹⁰⁰/₁₁₅

⇒ P = ^{4485 × 100}/₁₁₅

⇒ P = ⁴⁴⁸⁵⁰⁰/₁₁₅

⇒ P = $3900

Thus, the sum borrowed (P) = $3900 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 4485, then the Principal = ¹⁰⁰/₁₁₅ × 4485

= ^{100 × 4485}/₁₁₅

= ⁴⁴⁸⁵⁰⁰/₁₁₅

= 3900

Thus, Principal = $3900

Thus, the sum borrowed = $3900 Answer

Similar Questions

(1) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 9% simple interest?

(2) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 3 years.

(4) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 8% simple interest?

(5) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 9% simple interest?

(7) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?

(8) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8312.5 to clear it?

(9) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.

(10) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.