Simple Interest
Math MCQs

Question :    If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4550

Solution & Explanation

Solution

Given,

Amount (A) = $4914

Rate of Simple Interest (R) = 2%

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

$4914 = P (1 + 2% × 4)

⇒ $4914 = P (1 + ²/₁₀₀ × 4)

⇒ $4914 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4914 = P (1 + ⁸/₁₀₀)

⇒ $4914 = P (^{100 + 8}/₁₀₀)

⇒ $4914 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4914

⇒ P = ⁴⁹¹⁴/_¹⁰⁸/100

⇒ P = 4914 × ¹⁰⁰/₁₀₈

⇒ P = ^{4914 × 100}/₁₀₈

⇒ P = ⁴⁹¹⁴⁰⁰/₁₀₈

⇒ 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 4914, then the Principal = ¹⁰⁰/₁₀₈ × 4914

= ^{100 × 4914}/₁₀₈

= ⁴⁹¹⁴⁰⁰/₁₀₈

= 4550

Thus, Principal = $4550

Thus, the sum borrowed = $4550 Answer

Similar Questions

(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 7 years.

(2) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 2% simple interest?

(3) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 6% simple interest.

(4) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.

(5) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?

(6) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.

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

(8) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 8% simple interest?

(9) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 7% simple interest?

(10) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.