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) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 5% simple interest?

(2) How much loan did Deborah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8195 to clear it?

(3) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 3% simple interest?

(5) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.

(6) If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 8 years.

(8) What amount does David have to pay after 5 years if he takes a loan of $3400 at 8% simple interest?

(9) How much loan did John borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5720 to clear it?

(10) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 3 years.