Simple Interest
Math MCQs

Question :    Jennifer had to pay $3542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

Correct Answer  $3250

Solution & Explanation

Solution

Given,

Amount (A) = $3542.5

Rate of Simple Interest (R) = 3%

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

$3542.5 = P (1 + 3% × 3)

⇒ $3542.5 = P (1 + ³/₁₀₀ × 3)

⇒ $3542.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3542.5 = P (1 + ⁹/₁₀₀)

⇒ $3542.5 = P (^{100 + 9}/₁₀₀)

⇒ $3542.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3542.5

⇒ P = ^3542.5/_¹⁰⁹/100

⇒ P = 3542.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{3542.5 × 100}/₁₀₉

⇒ P = ³⁵⁴²⁵⁰/₁₀₉

⇒ P = $3250

Thus, the sum borrowed (P) = $3250 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 9

Thus, simple interest for 3 years = 9

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 9 = 109

Calculation of the Principal

Now,

∵ If the Amount is 109, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₉

∴ If the Amount is 3542.5, then the Principal = ¹⁰⁰/₁₀₉ × 3542.5

= ^{100 × 3542.5}/₁₀₉

= ³⁵⁴²⁵⁰/₁₀₉

= 3250

Thus, Principal = $3250

Thus, the sum borrowed = $3250 Answer

Similar Questions

(1) In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?

(2) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.

(3) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.

(4) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9800 to clear the loan, then find the time period of the loan.

(5) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10660 to clear the loan, then find the time period of the loan.

(6) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 7 years.

(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 7 years.

(9) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 4 years.

(10) Calculate the amount due if Michael borrowed a sum of $3300 at 4% simple interest for 4 years.