Simple Interest
Math MCQs

Question :    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) What amount will be due after 2 years if David borrowed a sum of $3200 at a 9% simple interest?

(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 3 years.

(3) In how much time a principal of $3150 will amount to $3465 at a simple interest of 2% per annum?

(4) Donna had to pay $5432 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 7% simple interest?

(6) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.

(7) How much loan did Sarah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7312.5 to clear it?

(8) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 7 years.

(9) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.