Simple Interest
Math MCQs

Question :    Michael had to pay $3795 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  $3300

Solution & Explanation

Solution

Given,

Amount (A) = $3795

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

$3795 = P (1 + 5% × 3)

⇒ $3795 = P (1 + ⁵/₁₀₀ × 3)

⇒ $3795 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $3795 = P (1 + ¹⁵/₁₀₀)

⇒ $3795 = P (^{100 + 15}/₁₀₀)

⇒ $3795 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $3795

⇒ P = ³⁷⁹⁵/_¹¹⁵/100

⇒ P = 3795 × ¹⁰⁰/₁₁₅

⇒ P = ^{3795 × 100}/₁₁₅

⇒ P = ³⁷⁹⁵⁰⁰/₁₁₅

⇒ P = $3300

Thus, the sum borrowed (P) = $3300 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 3795, then the Principal = ¹⁰⁰/₁₁₅ × 3795

= ^{100 × 3795}/₁₁₅

= ³⁷⁹⁵⁰⁰/₁₁₅

= 3300

Thus, Principal = $3300

Thus, the sum borrowed = $3300 Answer

Similar Questions

(1) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?

(2) What amount does James have to pay after 6 years if he takes a loan of $3000 at 6% simple interest?

(3) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.

(4) If Michael paid $3696 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 8 years.

(7) How much loan did Jason borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9625 to clear it?

(8) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 2% simple interest?

(9) If Kenneth paid $5600 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 9% simple interest.