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) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.

(2) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 8 years.

(3) If Margaret paid $5046 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(4) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?

(5) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8568 to clear the loan, then find the time period of the loan.

(6) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9062.5 to clear it?

(7) If Christopher paid $4480 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.

(9) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 8% simple interest?

(10) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5960 to clear the loan, then find the time period of the loan.