Simple Interest
Math MCQs

Question :    Betty had to pay $4887.5 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  $4250

Solution & Explanation

Solution

Given,

Amount (A) = $4887.5

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

$4887.5 = P (1 + 5% × 3)

⇒ $4887.5 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4887.5 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4887.5 = P (1 + ¹⁵/₁₀₀)

⇒ $4887.5 = P (^{100 + 15}/₁₀₀)

⇒ $4887.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4887.5

⇒ P = ^4887.5/_¹¹⁵/100

⇒ P = 4887.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{4887.5 × 100}/₁₁₅

⇒ P = ⁴⁸⁸⁷⁵⁰/₁₁₅

⇒ P = $4250

Thus, the sum borrowed (P) = $4250 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 4887.5, then the Principal = ¹⁰⁰/₁₁₅ × 4887.5

= ^{100 × 4887.5}/₁₁₅

= ⁴⁸⁸⁷⁵⁰/₁₁₅

= 4250

Thus, Principal = $4250

Thus, the sum borrowed = $4250 Answer

Similar Questions

(1) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 8 years.

(3) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.

(4) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 3 years.

(5) What amount does David have to pay after 5 years if he takes a loan of $3400 at 3% simple interest?

(6) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 4% simple interest?

(7) How much loan did Anthony borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7560 to clear it?

(8) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) In how much time a principal of $3150 will amount to $3465 at a simple interest of 5% per annum?

(10) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12670 to clear the loan, then find the time period of the loan.