Simple Interest
Math MCQs

Question :    How much loan did Dorothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7975 to clear it?

Correct Answer  $7250

Solution & Explanation

Solution

Given,

Amount (A) = $7975

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

$7975 = P (1 + 2% × 5)

⇒ $7975 = P (1 + ²/₁₀₀ × 5)

⇒ $7975 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7975 = P (1 + ¹⁰/₁₀₀)

⇒ $7975 = P (^{100 + 10}/₁₀₀)

⇒ $7975 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7975

⇒ P = ⁷⁹⁷⁵/_¹¹⁰/100

⇒ P = 7975 × ¹⁰⁰/₁₁₀

⇒ P = ^{7975 × 100}/₁₁₀

⇒ P = ⁷⁹⁷⁵⁰⁰/₁₁₀

⇒ P = $7250

Thus, the sum borrowed (P) = $7250 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 7975, then the Principal = ¹⁰⁰/₁₁₀ × 7975

= ^{100 × 7975}/₁₁₀

= ⁷⁹⁷⁵⁰⁰/₁₁₀

= 7250

Thus, Principal = $7250

Thus, the sum borrowed = $7250 Answer

Similar Questions

(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 8 years.

(2) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 2% simple interest.

(4) Andrew had to pay $5232 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 7 years.

(6) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 3% simple interest?

(7) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 8 years.

(9) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.

(10) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?