Simple Interest
Math MCQs

Question :    If Mary paid $3416 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3050

Solution & Explanation

Solution

Given,

Amount (A) = $3416

Rate of Simple Interest (R) = 3%

Time (T) = 4 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 + 3% × 4)

⇒ $3416 = P (1 + ³/₁₀₀ × 4)

⇒ $3416 = P (1 + ^{3 × 4}/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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 3 = 12

Thus, simple interest for 4 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) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8050 to clear it?

(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 3 years.

(3) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 3 years.

(4) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.

(5) In how much time a principal of $3000 will amount to $3600 at a simple interest of 4% per annum?

(6) How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?

(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 7 years.

(8) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 7% simple interest?

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

(10) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.