Simple Interest
Math MCQs

Question :    How much loan did Sarah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6435 to clear it?

Correct Answer  $5850

Solution & Explanation

Solution

Given,

Amount (A) = $6435

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

$6435 = P (1 + 2% × 5)

⇒ $6435 = P (1 + ²/₁₀₀ × 5)

⇒ $6435 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6435 = P (1 + ¹⁰/₁₀₀)

⇒ $6435 = P (^{100 + 10}/₁₀₀)

⇒ $6435 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6435

⇒ P = ⁶⁴³⁵/_¹¹⁰/100

⇒ P = 6435 × ¹⁰⁰/₁₁₀

⇒ P = ^{6435 × 100}/₁₁₀

⇒ P = ⁶⁴³⁵⁰⁰/₁₁₀

⇒ P = $5850

Thus, the sum borrowed (P) = $5850 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 6435, then the Principal = ¹⁰⁰/₁₁₀ × 6435

= ^{100 × 6435}/₁₁₀

= ⁶⁴³⁵⁰⁰/₁₁₀

= 5850

Thus, Principal = $5850

Thus, the sum borrowed = $5850 Answer

Similar Questions

(1) If Susan paid $4234 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 7 years.

(3) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 9% simple interest?

(4) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.

(5) How much loan did Joshua borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7590 to clear it?

(6) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?

(7) If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 7 years.

(10) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 4% simple interest?