Simple Interest
Math MCQs

Question :    If Kimberly paid $5580 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4650

Solution & Explanation

Solution

Given,

Amount (A) = $5580

Rate of Simple Interest (R) = 5%

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

$5580 = P (1 + 5% × 4)

⇒ $5580 = P (1 + ⁵/₁₀₀ × 4)

⇒ $5580 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $5580 = P (1 + ²⁰/₁₀₀)

⇒ $5580 = P (^{100 + 20}/₁₀₀)

⇒ $5580 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $5580

⇒ P = ⁵⁵⁸⁰/_¹²⁰/100

⇒ P = 5580 × ¹⁰⁰/₁₂₀

⇒ P = ^{5580 × 100}/₁₂₀

⇒ P = ⁵⁵⁸⁰⁰⁰/₁₂₀

⇒ 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 20

Thus, simple interest for 4 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 5580, then the Principal = ¹⁰⁰/₁₂₀ × 5580

= ^{100 × 5580}/₁₂₀

= ⁵⁵⁸⁰⁰⁰/₁₂₀

= 4650

Thus, Principal = $4650

Thus, the sum borrowed = $4650 Answer

Similar Questions

(1) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

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

(3) What amount does David have to pay after 5 years if he takes a loan of $3400 at 9% simple interest?

(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.

(5) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.

(6) If Susan paid $4088 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) What amount does David have to pay after 6 years if he takes a loan of $3400 at 4% simple interest?

(8) How much loan did Jessica borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6325 to clear it?

(9) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 8 years.

(10) Joseph had to pay $4255 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.