Simple Interest
Math MCQs

Question :    How much loan did Michael borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5830 to clear it?

Correct Answer  $5300

Solution & Explanation

Solution

Given,

Amount (A) = $5830

Rate of Simple Interest (R) = 2%

Time (T) = 5 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

$5830 = P (1 + 2% × 5)

⇒ $5830 = P (1 + ²/₁₀₀ × 5)

⇒ $5830 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $5830 = P (1 + ¹⁰/₁₀₀)

⇒ $5830 = P (^{100 + 10}/₁₀₀)

⇒ $5830 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $5830

⇒ P = ⁵⁸³⁰/_¹¹⁰/100

⇒ P = 5830 × ¹⁰⁰/₁₁₀

⇒ P = ^{5830 × 100}/₁₁₀

⇒ P = ⁵⁸³⁰⁰⁰/₁₁₀

⇒ P = $5300

Thus, the sum borrowed (P) = $5300 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 = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 5830, then the Principal = ¹⁰⁰/₁₁₀ × 5830

= ^{100 × 5830}/₁₁₀

= ⁵⁸³⁰⁰⁰/₁₁₀

= 5300

Thus, Principal = $5300

Thus, the sum borrowed = $5300 Answer

Similar Questions

(1) If Michael paid $3960 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 4% simple interest?

(3) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 9% simple interest?

(4) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.

(5) How much loan did Donald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7475 to clear it?

(6) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?

(7) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?

(8) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.

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

(10) Susan had to pay $3978.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.