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) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 8 years.

(2) In how much time a principal of $3100 will amount to $3348 at a simple interest of 2% per annum?

(3) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 6% simple interest.

(4) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.

(5) If Charles borrowed $3900 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(6) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.

(7) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.

(8) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 7% simple interest?

(9) How much loan did Amanda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8222.5 to clear it?

(10) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 4 years.