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) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 4 years.

(2) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.

(3) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7152 to clear the loan, then find the time period of the loan.

(4) If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(5) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 6% simple interest?

(6) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.

(8) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.

(9) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.

(10) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?