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) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 8% simple interest?

(2) How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?

(3) How much loan did David borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6210 to clear it?

(4) In how much time a principal of $3150 will amount to $3339 at a simple interest of 2% per annum?

(5) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 4% simple interest?

(6) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?

(7) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.

(9) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.

(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 4 years.