Simple Interest
Math MCQs

Question :    David had to pay $3808 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $3400

Solution & Explanation

Solution

Given,

Amount (A) = $3808

Rate of Simple Interest (R) = 4%

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

$3808 = P (1 + 4% × 3)

⇒ $3808 = P (1 + ⁴/₁₀₀ × 3)

⇒ $3808 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $3808 = P (1 + ¹²/₁₀₀)

⇒ $3808 = P (^{100 + 12}/₁₀₀)

⇒ $3808 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3808

⇒ P = ³⁸⁰⁸/_¹¹²/100

⇒ P = 3808 × ¹⁰⁰/₁₁₂

⇒ P = ^{3808 × 100}/₁₁₂

⇒ P = ³⁸⁰⁸⁰⁰/₁₁₂

⇒ P = $3400

Thus, the sum borrowed (P) = $3400 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 12

Thus, simple interest for 3 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 3808, then the Principal = ¹⁰⁰/₁₁₂ × 3808

= ^{100 × 3808}/₁₁₂

= ³⁸⁰⁸⁰⁰/₁₁₂

= 3400

Thus, Principal = $3400

Thus, the sum borrowed = $3400 Answer

Similar Questions

(1) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 8 years.

(2) What amount does John have to pay after 5 years if he takes a loan of $3200 at 9% simple interest?

(3) What amount does James have to pay after 6 years if he takes a loan of $3000 at 8% simple interest?

(4) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.

(6) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 4 years.

(7) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.

(8) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.

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

(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 7 years.