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) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 4 years.

(2) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.

(4) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 3 years.

(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 8 years.

(7) In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?

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

(9) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.

(10) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $5984 to clear the loan, then find the time period of the loan.