Simple Interest
Math MCQs

Question :    If Margaret paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4350

Solution & Explanation

Solution

Given,

Amount (A) = $4698

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

$4698 = P (1 + 2% × 4)

⇒ $4698 = P (1 + ²/₁₀₀ × 4)

⇒ $4698 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4698 = P (1 + ⁸/₁₀₀)

⇒ $4698 = P (^{100 + 8}/₁₀₀)

⇒ $4698 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4698

⇒ P = ⁴⁶⁹⁸/_¹⁰⁸/100

⇒ P = 4698 × ¹⁰⁰/₁₀₈

⇒ P = ^{4698 × 100}/₁₀₈

⇒ P = ⁴⁶⁹⁸⁰⁰/₁₀₈

⇒ P = $4350

Thus, the sum borrowed (P) = $4350 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 4698, then the Principal = ¹⁰⁰/₁₀₈ × 4698

= ^{100 × 4698}/₁₀₈

= ⁴⁶⁹⁸⁰⁰/₁₀₈

= 4350

Thus, Principal = $4350

Thus, the sum borrowed = $4350 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.

(2) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 3 years.

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

(4) James had to pay $3360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 3 years.

(6) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 10% simple interest?

(7) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 3 years.

(8) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.

(9) In how much time a principal of $3050 will amount to $3416 at a simple interest of 3% per annum?

(10) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 7% simple interest?