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) In how much time a principal of $3000 will amount to $3480 at a simple interest of 4% per annum?

(2) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?

(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 8 years.

(4) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 8 years.

(5) If Michelle paid $5346 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 7 years.

(7) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.

(8) What amount does David have to pay after 6 years if he takes a loan of $3400 at 8% simple interest?

(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 8 years.

(10) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?