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) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.

(2) What amount does David have to pay after 5 years if he takes a loan of $3400 at 6% simple interest?

(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 5% simple interest?

(4) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.

(5) If Steven paid $5336 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

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

(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 4% simple interest?

(8) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?

(9) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.

(10) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 6% simple interest?