Simple Interest
Math MCQs

Question :    Donald had to pay $4770 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $4500

Solution & Explanation

Solution

Given,

Amount (A) = $4770

Rate of Simple Interest (R) = 2%

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

$4770 = P (1 + 2% × 3)

⇒ $4770 = P (1 + ²/₁₀₀ × 3)

⇒ $4770 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $4770 = P (1 + ⁶/₁₀₀)

⇒ $4770 = P (^{100 + 6}/₁₀₀)

⇒ $4770 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $4770

⇒ P = ⁴⁷⁷⁰/_¹⁰⁶/100

⇒ P = 4770 × ¹⁰⁰/₁₀₆

⇒ P = ^{4770 × 100}/₁₀₆

⇒ P = ⁴⁷⁷⁰⁰⁰/₁₀₆

⇒ P = $4500

Thus, the sum borrowed (P) = $4500 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 4770, then the Principal = ¹⁰⁰/₁₀₆ × 4770

= ^{100 × 4770}/₁₀₆

= ⁴⁷⁷⁰⁰⁰/₁₀₆

= 4500

Thus, Principal = $4500

Thus, the sum borrowed = $4500 Answer

Similar Questions

(1) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?

(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 9% simple interest?

(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 3 years.

(4) Daniel had to pay $4346 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 8 years.

(6) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 3 years.

(7) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 10% simple interest.

(8) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 3 years.

(9) If Michael borrowed $3300 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(10) In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?