Simple Interest
Math MCQs

Question :    How much loan did Dorothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8337.5 to clear it?

Correct Answer  $7250

Solution & Explanation

Solution

Given,

Amount (A) = $8337.5

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

$8337.5 = P (1 + 3% × 5)

⇒ $8337.5 = P (1 + ³/₁₀₀ × 5)

⇒ $8337.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8337.5 = P (1 + ¹⁵/₁₀₀)

⇒ $8337.5 = P (^{100 + 15}/₁₀₀)

⇒ $8337.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8337.5

⇒ P = ^8337.5/_¹¹⁵/100

⇒ P = 8337.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{8337.5 × 100}/₁₁₅

⇒ P = ⁸³³⁷⁵⁰/₁₁₅

⇒ P = $7250

Thus, the sum borrowed (P) = $7250 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 8337.5, then the Principal = ¹⁰⁰/₁₁₅ × 8337.5

= ^{100 × 8337.5}/₁₁₅

= ⁸³³⁷⁵⁰/₁₁₅

= 7250

Thus, Principal = $7250

Thus, the sum borrowed = $7250 Answer

Similar Questions

(1) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.

(2) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?

(3) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 8% simple interest.

(4) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?

(5) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 10% simple interest?

(6) If Lisa paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) Andrew had to pay $5232 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.

(9) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.

(10) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.