Simple Interest
Math MCQs

Question :    If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3950

Solution & Explanation

Solution

Given,

Amount (A) = $4582

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

$4582 = P (1 + 4% × 4)

⇒ $4582 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4582 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4582 = P (1 + ¹⁶/₁₀₀)

⇒ $4582 = P (^{100 + 16}/₁₀₀)

⇒ $4582 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4582

⇒ P = ⁴⁵⁸²/_¹¹⁶/100

⇒ P = 4582 × ¹⁰⁰/₁₁₆

⇒ P = ^{4582 × 100}/₁₁₆

⇒ P = ⁴⁵⁸²⁰⁰/₁₁₆

⇒ P = $3950

Thus, the sum borrowed (P) = $3950 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 4582, then the Principal = ¹⁰⁰/₁₁₆ × 4582

= ^{100 × 4582}/₁₁₆

= ⁴⁵⁸²⁰⁰/₁₁₆

= 3950

Thus, Principal = $3950

Thus, the sum borrowed = $3950 Answer

Similar Questions

(1) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6037.5 to clear it?

(2) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 3% simple interest?

(3) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?

(4) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?

(5) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 5% per annum?

(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.

(8) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.

(9) What amount does John have to pay after 6 years if he takes a loan of $3200 at 7% simple interest?

(10) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7301 to clear the loan, then find the time period of the loan.