Simple Interest
Math MCQs

Question :    Richard had to pay $3816 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  $3600

Solution & Explanation

Solution

Given,

Amount (A) = $3816

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

$3816 = P (1 + 2% × 3)

⇒ $3816 = P (1 + ²/₁₀₀ × 3)

⇒ $3816 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3816 = P (1 + ⁶/₁₀₀)

⇒ $3816 = P (^{100 + 6}/₁₀₀)

⇒ $3816 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3816

⇒ P = ³⁸¹⁶/_¹⁰⁶/100

⇒ P = 3816 × ¹⁰⁰/₁₀₆

⇒ P = ^{3816 × 100}/₁₀₆

⇒ P = ³⁸¹⁶⁰⁰/₁₀₆

⇒ P = $3600

Thus, the sum borrowed (P) = $3600 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 3816, then the Principal = ¹⁰⁰/₁₀₆ × 3816

= ^{100 × 3816}/₁₀₆

= ³⁸¹⁶⁰⁰/₁₀₆

= 3600

Thus, Principal = $3600

Thus, the sum borrowed = $3600 Answer

Similar Questions

(1) How much loan did Charles borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7375 to clear it?

(2) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 8% simple interest?

(3) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.

(5) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 3% simple interest?

(6) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 7% simple interest?

(7) How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?

(8) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.

(9) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 3 years.