Simple Interest
Math MCQs

Question :    If Betty paid $4590 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4250

Solution & Explanation

Solution

Given,

Amount (A) = $4590

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

$4590 = P (1 + 2% × 4)

⇒ $4590 = P (1 + ²/₁₀₀ × 4)

⇒ $4590 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4590 = P (1 + ⁸/₁₀₀)

⇒ $4590 = P (^{100 + 8}/₁₀₀)

⇒ $4590 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4590

⇒ P = ⁴⁵⁹⁰/_¹⁰⁸/100

⇒ P = 4590 × ¹⁰⁰/₁₀₈

⇒ P = ^{4590 × 100}/₁₀₈

⇒ P = ⁴⁵⁹⁰⁰⁰/₁₀₈

⇒ P = $4250

Thus, the sum borrowed (P) = $4250 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 4590, then the Principal = ¹⁰⁰/₁₀₈ × 4590

= ^{100 × 4590}/₁₀₈

= ⁴⁵⁹⁰⁰⁰/₁₀₈

= 4250

Thus, Principal = $4250

Thus, the sum borrowed = $4250 Answer

Similar Questions

(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 8 years.

(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 8 years.

(3) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?

(4) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?

(5) William had to pay $4025 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.

(7) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 2% simple interest?

(8) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 8% simple interest?

(9) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 3 years.

(10) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 7% simple interest?