Simple Interest
Math MCQs

Question :    How much loan did Ashley borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7205 to clear it?

Correct Answer  $6550

Solution & Explanation

Solution

Given,

Amount (A) = $7205

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

$7205 = P (1 + 2% × 5)

⇒ $7205 = P (1 + ²/₁₀₀ × 5)

⇒ $7205 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7205 = P (1 + ¹⁰/₁₀₀)

⇒ $7205 = P (^{100 + 10}/₁₀₀)

⇒ $7205 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7205

⇒ P = ⁷²⁰⁵/_¹¹⁰/100

⇒ P = 7205 × ¹⁰⁰/₁₁₀

⇒ P = ^{7205 × 100}/₁₁₀

⇒ P = ⁷²⁰⁵⁰⁰/₁₁₀

⇒ P = $6550

Thus, the sum borrowed (P) = $6550 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 7205, then the Principal = ¹⁰⁰/₁₁₀ × 7205

= ^{100 × 7205}/₁₁₀

= ⁷²⁰⁵⁰⁰/₁₁₀

= 6550

Thus, Principal = $6550

Thus, the sum borrowed = $6550 Answer

Similar Questions

(1) Sarah had to pay $4081 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 3 years.

(3) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 4 years.

(5) How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?

(6) In how much time a principal of $3150 will amount to $3528 at a simple interest of 3% per annum?

(7) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.

(8) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 8 years.

(10) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.