Simple Interest
Math MCQs

Question :  ( 1 of 10 )  Mary had to pay $3324.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

Correct Answer  $3050

Solution & Explanation

Solution

Given,

Amount (A) = $3324.5

Rate of Simple Interest (R) = 3%

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

$3324.5 = P (1 + 3% × 3)

⇒ $3324.5 = P (1 + ³/₁₀₀ × 3)

⇒ $3324.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3324.5 = P (1 + ⁹/₁₀₀)

⇒ $3324.5 = P (^{100 + 9}/₁₀₀)

⇒ $3324.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3324.5

⇒ P = ^3324.5/_¹⁰⁹/100

⇒ P = 3324.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{3324.5 × 100}/₁₀₉

⇒ P = ³³²⁴⁵⁰/₁₀₉

⇒ P = $3050

Thus, the sum borrowed (P) = $3050 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 = 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 × 3 = 9

Thus, simple interest for 3 years = 9

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 9 = 109

Calculation of the Principal

Now,

∵ If the Amount is 109, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₉

∴ If the Amount is 3324.5, then the Principal = ¹⁰⁰/₁₀₉ × 3324.5

= ^{100 × 3324.5}/₁₀₉

= ³³²⁴⁵⁰/₁₀₉

= 3050

Thus, Principal = $3050

Thus, the sum borrowed = $3050 Answer

Similar Questions

(1) How much loan did Anthony borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7875 to clear it?

(2) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 7 years.

(3) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 9% simple interest?

(5) How much loan did Sharon borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9687.5 to clear it?

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

(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 7 years.

(8) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.

(9) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 4% simple interest?

(10) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.