Simple Interest
Math MCQs

Question :    Mary had to pay $3416 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  $3050

Solution & Explanation

Solution

Given,

Amount (A) = $3416

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

$3416 = P (1 + 4% × 3)

⇒ $3416 = P (1 + ⁴/₁₀₀ × 3)

⇒ $3416 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $3416 = P (1 + ¹²/₁₀₀)

⇒ $3416 = P (^{100 + 12}/₁₀₀)

⇒ $3416 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3416

⇒ P = ³⁴¹⁶/_¹¹²/100

⇒ P = 3416 × ¹⁰⁰/₁₁₂

⇒ P = ^{3416 × 100}/₁₁₂

⇒ P = ³⁴¹⁶⁰⁰/₁₁₂

⇒ 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 = 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 3416, then the Principal = ¹⁰⁰/₁₁₂ × 3416

= ^{100 × 3416}/₁₁₂

= ³⁴¹⁶⁰⁰/₁₁₂

= 3050

Thus, Principal = $3050

Thus, the sum borrowed = $3050 Answer

Similar Questions

(1) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 7 years.

(2) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 6% simple interest?

(3) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.

(4) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 8 years.

(6) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.

(7) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?

(8) Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 3 years.