Simple Interest
Math MCQs

Question :    Jessica had to pay $4087.5 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  $3750

Solution & Explanation

Solution

Given,

Amount (A) = $4087.5

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

$4087.5 = P (1 + 3% × 3)

⇒ $4087.5 = P (1 + ³/₁₀₀ × 3)

⇒ $4087.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4087.5 = P (1 + ⁹/₁₀₀)

⇒ $4087.5 = P (^{100 + 9}/₁₀₀)

⇒ $4087.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4087.5

⇒ P = ^4087.5/_¹⁰⁹/100

⇒ P = 4087.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{4087.5 × 100}/₁₀₉

⇒ P = ⁴⁰⁸⁷⁵⁰/₁₀₉

⇒ P = $3750

Thus, the sum borrowed (P) = $3750 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 4087.5, then the Principal = ¹⁰⁰/₁₀₉ × 4087.5

= ^{100 × 4087.5}/₁₀₉

= ⁴⁰⁸⁷⁵⁰/₁₀₉

= 3750

Thus, Principal = $3750

Thus, the sum borrowed = $3750 Answer

Similar Questions

(1) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.

(2) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 3 years.

(4) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 8% simple interest?

(5) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?

(6) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.

(7) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 8% simple interest?

(8) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.

(9) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.