Simple Interest
Math MCQs

Question :    If Kimberly paid $5394 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4650

Solution & Explanation

Solution

Given,

Amount (A) = $5394

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

$5394 = P (1 + 4% × 4)

⇒ $5394 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5394 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5394 = P (1 + ¹⁶/₁₀₀)

⇒ $5394 = P (^{100 + 16}/₁₀₀)

⇒ $5394 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5394

⇒ P = ⁵³⁹⁴/_¹¹⁶/100

⇒ P = 5394 × ¹⁰⁰/₁₁₆

⇒ P = ^{5394 × 100}/₁₁₆

⇒ P = ⁵³⁹⁴⁰⁰/₁₁₆

⇒ P = $4650

Thus, the sum borrowed (P) = $4650 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 5394, then the Principal = ¹⁰⁰/₁₁₆ × 5394

= ^{100 × 5394}/₁₁₆

= ⁵³⁹⁴⁰⁰/₁₁₆

= 4650

Thus, Principal = $4650

Thus, the sum borrowed = $4650 Answer

Similar Questions

(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 4 years.

(2) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6300 to clear it?

(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?

(4) How much loan did Patricia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6437.5 to clear it?

(5) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.

(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 8 years.

(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 8 years.

(8) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.

(9) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(10) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7421 to clear the loan, then find the time period of the loan.