Simple Interest
Math MCQs

Question :    If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3300

Solution & Explanation

Solution

Given,

Amount (A) = $3828

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

$3828 = P (1 + 4% × 4)

⇒ $3828 = P (1 + ⁴/₁₀₀ × 4)

⇒ $3828 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $3828 = P (1 + ¹⁶/₁₀₀)

⇒ $3828 = P (^{100 + 16}/₁₀₀)

⇒ $3828 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $3828

⇒ P = ³⁸²⁸/_¹¹⁶/100

⇒ P = 3828 × ¹⁰⁰/₁₁₆

⇒ P = ^{3828 × 100}/₁₁₆

⇒ P = ³⁸²⁸⁰⁰/₁₁₆

⇒ P = $3300

Thus, the sum borrowed (P) = $3300 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 3828, then the Principal = ¹⁰⁰/₁₁₆ × 3828

= ^{100 × 3828}/₁₁₆

= ³⁸²⁸⁰⁰/₁₁₆

= 3300

Thus, Principal = $3300

Thus, the sum borrowed = $3300 Answer

Similar Questions

(1) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 4% simple interest?

(2) Anthony had to pay $4816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) How much loan did Steven borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7590 to clear it?

(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 4 years.

(5) What amount does John have to pay after 5 years if he takes a loan of $3200 at 6% simple interest?

(6) Karen had to pay $4424 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?

(8) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 3 years.

(9) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 4% simple interest?

(10) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.