Simple Interest
Math MCQs

Question :    Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

Correct Answer  $4950

Solution & Explanation

Solution

Given,

Amount (A) = $5692.5

Rate of Simple Interest (R) = 5%

Time (T) = 3 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

$5692.5 = P (1 + 5% × 3)

⇒ $5692.5 = P (1 + ⁵/₁₀₀ × 3)

⇒ $5692.5 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $5692.5 = P (1 + ¹⁵/₁₀₀)

⇒ $5692.5 = P (^{100 + 15}/₁₀₀)

⇒ $5692.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5692.5

⇒ P = ^5692.5/_¹¹⁵/100

⇒ P = 5692.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{5692.5 × 100}/₁₁₅

⇒ P = ⁵⁶⁹²⁵⁰/₁₁₅

⇒ P = $4950

Thus, the sum borrowed (P) = $4950 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

Calculation of the Amount

Since, in the question, time = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 5 = 15

Thus, simple interest for 3 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 5692.5, then the Principal = ¹⁰⁰/₁₁₅ × 5692.5

= ^{100 × 5692.5}/₁₁₅

= ⁵⁶⁹²⁵⁰/₁₁₅

= 4950

Thus, Principal = $4950

Thus, the sum borrowed = $4950 Answer

Similar Questions

(1) What amount will be due after 2 years if David borrowed a sum of $3200 at a 8% simple interest?

(2) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.

(3) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.

(4) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.

(5) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.

(6) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.

(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 4 years.

(9) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 8 years.