Simple Interest
Math MCQs

Question :    How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?

Correct Answer  $7050

Solution & Explanation

Solution

Given,

Amount (A) = $7755

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

$7755 = P (1 + 2% × 5)

⇒ $7755 = P (1 + ²/₁₀₀ × 5)

⇒ $7755 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7755 = P (1 + ¹⁰/₁₀₀)

⇒ $7755 = P (^{100 + 10}/₁₀₀)

⇒ $7755 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7755

⇒ P = ⁷⁷⁵⁵/_¹¹⁰/100

⇒ P = 7755 × ¹⁰⁰/₁₁₀

⇒ P = ^{7755 × 100}/₁₁₀

⇒ P = ⁷⁷⁵⁵⁰⁰/₁₁₀

⇒ P = $7050

Thus, the sum borrowed (P) = $7050 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 7755, then the Principal = ¹⁰⁰/₁₁₀ × 7755

= ^{100 × 7755}/₁₁₀

= ⁷⁷⁵⁵⁰⁰/₁₁₀

= 7050

Thus, Principal = $7050

Thus, the sum borrowed = $7050 Answer

Similar Questions

(1) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 7% simple interest?

(2) Calculate the amount due if Linda borrowed a sum of $3350 at 6% simple interest for 4 years.

(3) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.

(4) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.

(5) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 2% simple interest?

(6) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 7 years.

(8) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.

(9) How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?

(10) What amount will be due after 2 years if William borrowed a sum of $3250 at a 10% simple interest?