Simple Interest
Math MCQs

Question :    Jessica had to pay $3975 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $3750

Solution & Explanation

Solution

Given,

Amount (A) = $3975

Rate of Simple Interest (R) = 2%

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

$3975 = P (1 + 2% × 3)

⇒ $3975 = P (1 + ²/₁₀₀ × 3)

⇒ $3975 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3975 = P (1 + ⁶/₁₀₀)

⇒ $3975 = P (^{100 + 6}/₁₀₀)

⇒ $3975 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3975

⇒ P = ³⁹⁷⁵/_¹⁰⁶/100

⇒ P = 3975 × ¹⁰⁰/₁₀₆

⇒ P = ^{3975 × 100}/₁₀₆

⇒ P = ³⁹⁷⁵⁰⁰/₁₀₆

⇒ 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 = 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 = 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 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 3975, then the Principal = ¹⁰⁰/₁₀₆ × 3975

= ^{100 × 3975}/₁₀₆

= ³⁹⁷⁵⁰⁰/₁₀₆

= 3750

Thus, Principal = $3750

Thus, the sum borrowed = $3750 Answer

Similar Questions

(1) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 3% simple interest?

(3) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 4 years.

(5) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.

(6) How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?

(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.

(8) How much loan did Ryan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9875 to clear it?

(9) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 4% simple interest?

(10) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?