Simple Interest
Math MCQs

Question :    How much loan did Barbara borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6382.5 to clear it?

Correct Answer  $5550

Solution & Explanation

Solution

Given,

Amount (A) = $6382.5

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

$6382.5 = P (1 + 3% × 5)

⇒ $6382.5 = P (1 + ³/₁₀₀ × 5)

⇒ $6382.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6382.5 = P (1 + ¹⁵/₁₀₀)

⇒ $6382.5 = P (^{100 + 15}/₁₀₀)

⇒ $6382.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6382.5

⇒ P = ^6382.5/_¹¹⁵/100

⇒ P = 6382.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{6382.5 × 100}/₁₁₅

⇒ P = ⁶³⁸²⁵⁰/₁₁₅

⇒ P = $5550

Thus, the sum borrowed (P) = $5550 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 6382.5, then the Principal = ¹⁰⁰/₁₁₅ × 6382.5

= ^{100 × 6382.5}/₁₁₅

= ⁶³⁸²⁵⁰/₁₁₅

= 5550

Thus, Principal = $5550

Thus, the sum borrowed = $5550 Answer

Similar Questions

(1) What amount does James have to pay after 5 years if he takes a loan of $3000 at 8% simple interest?

(2) How much loan did David borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6750 to clear it?

(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 8 years.

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

(5) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.

(6) If Richard paid $3888 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.

(8) How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?

(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.

(10) In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum?