Simple Interest
Math MCQs

Question :    Kimberly had to pay $5068.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

Correct Answer  $4650

Solution & Explanation

Solution

Given,

Amount (A) = $5068.5

Rate of Simple Interest (R) = 3%

Time (T) = 3 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

$5068.5 = P (1 + 3% × 3)

⇒ $5068.5 = P (1 + ³/₁₀₀ × 3)

⇒ $5068.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $5068.5 = P (1 + ⁹/₁₀₀)

⇒ $5068.5 = P (^{100 + 9}/₁₀₀)

⇒ $5068.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $5068.5

⇒ P = ^5068.5/_¹⁰⁹/100

⇒ P = 5068.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{5068.5 × 100}/₁₀₉

⇒ P = ⁵⁰⁶⁸⁵⁰/₁₀₉

⇒ 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

Calculation of the Amount

Since, in the question, time = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 3 = 9

Thus, simple interest for 3 years = 9

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 9 = 109

Calculation of the Principal

Now,

∵ If the Amount is 109, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₉

∴ If the Amount is 5068.5, then the Principal = ¹⁰⁰/₁₀₉ × 5068.5

= ^{100 × 5068.5}/₁₀₉

= ⁵⁰⁶⁸⁵⁰/₁₀₉

= 4650

Thus, Principal = $4650

Thus, the sum borrowed = $4650 Answer

Similar Questions

(1) If Michael paid $3696 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 8 years.

(3) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6528 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 8% simple interest.

(5) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.

(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 2% simple interest.

(7) In how much time a principal of $3150 will amount to $3433.5 at a simple interest of 3% per annum?

(8) How much loan did Ashley borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7205 to clear it?

(9) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 5% simple interest?

(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 8 years.