Simple Interest
Math MCQs

Question :    If Daniel paid $4428 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4100

Solution & Explanation

Solution

Given,

Amount (A) = $4428

Rate of Simple Interest (R) = 2%

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

$4428 = P (1 + 2% × 4)

⇒ $4428 = P (1 + ²/₁₀₀ × 4)

⇒ $4428 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4428 = P (1 + ⁸/₁₀₀)

⇒ $4428 = P (^{100 + 8}/₁₀₀)

⇒ $4428 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4428

⇒ P = ⁴⁴²⁸/_¹⁰⁸/100

⇒ P = 4428 × ¹⁰⁰/₁₀₈

⇒ P = ^{4428 × 100}/₁₀₈

⇒ P = ⁴⁴²⁸⁰⁰/₁₀₈

⇒ P = $4100

Thus, the sum borrowed (P) = $4100 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 = 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 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 4428, then the Principal = ¹⁰⁰/₁₀₈ × 4428

= ^{100 × 4428}/₁₀₈

= ⁴⁴²⁸⁰⁰/₁₀₈

= 4100

Thus, Principal = $4100

Thus, the sum borrowed = $4100 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.

(2) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.

(3) Thomas had to pay $4256 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 6% simple interest?

(6) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 4 years.

(8) In how much time a principal of $3100 will amount to $3720 at a simple interest of 4% per annum?

(9) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 4 years.

(10) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 4% simple interest?