Simple Interest
Math MCQs

Question :    If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4550

Solution & Explanation

Solution

Given,

Amount (A) = $5096

Rate of Simple Interest (R) = 3%

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

$5096 = P (1 + 3% × 4)

⇒ $5096 = P (1 + ³/₁₀₀ × 4)

⇒ $5096 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $5096 = P (1 + ¹²/₁₀₀)

⇒ $5096 = P (^{100 + 12}/₁₀₀)

⇒ $5096 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5096

⇒ P = ⁵⁰⁹⁶/_¹¹²/100

⇒ P = 5096 × ¹⁰⁰/₁₁₂

⇒ P = ^{5096 × 100}/₁₁₂

⇒ P = ⁵⁰⁹⁶⁰⁰/₁₁₂

⇒ P = $4550

Thus, the sum borrowed (P) = $4550 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 = 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 × 3 = 12

Thus, simple interest for 4 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 5096, then the Principal = ¹⁰⁰/₁₁₂ × 5096

= ^{100 × 5096}/₁₁₂

= ⁵⁰⁹⁶⁰⁰/₁₁₂

= 4550

Thus, Principal = $4550

Thus, the sum borrowed = $4550 Answer

Similar Questions

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

(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 8 years.

(3) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.

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

(5) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.

(6) How much loan did Edward borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8360 to clear it?

(7) Jennifer had to pay $3445 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(8) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.

(9) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 4% simple interest?

(10) What amount does David have to pay after 5 years if he takes a loan of $3400 at 4% simple interest?