Simple Interest
Math MCQs

Question :    If Nancy paid $4814 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4150

Solution & Explanation

Solution

Given,

Amount (A) = $4814

Rate of Simple Interest (R) = 4%

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

$4814 = P (1 + 4% × 4)

⇒ $4814 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4814 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4814 = P (1 + ¹⁶/₁₀₀)

⇒ $4814 = P (^{100 + 16}/₁₀₀)

⇒ $4814 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4814

⇒ P = ⁴⁸¹⁴/_¹¹⁶/100

⇒ P = 4814 × ¹⁰⁰/₁₁₆

⇒ P = ^{4814 × 100}/₁₁₆

⇒ P = ⁴⁸¹⁴⁰⁰/₁₁₆

⇒ P = $4150

Thus, the sum borrowed (P) = $4150 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 = 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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 4814, then the Principal = ¹⁰⁰/₁₁₆ × 4814

= ^{100 × 4814}/₁₁₆

= ⁴⁸¹⁴⁰⁰/₁₁₆

= 4150

Thus, Principal = $4150

Thus, the sum borrowed = $4150 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.

(2) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 4 years.

(3) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 5% simple interest?

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

(5) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 8% simple interest?

(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 3 years.

(7) What amount does David have to pay after 6 years if he takes a loan of $3400 at 3% simple interest?

(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?

(9) Ashley had to pay $4823 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 4 years.