Simple Interest
Math MCQs

Question :    William had to pay $3920 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $3500

Solution & Explanation

Solution

Given,

Amount (A) = $3920

Rate of Simple Interest (R) = 4%

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

$3920 = P (1 + 4% × 3)

⇒ $3920 = P (1 + ⁴/₁₀₀ × 3)

⇒ $3920 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $3920 = P (1 + ¹²/₁₀₀)

⇒ $3920 = P (^{100 + 12}/₁₀₀)

⇒ $3920 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3920

⇒ P = ³⁹²⁰/_¹¹²/100

⇒ P = 3920 × ¹⁰⁰/₁₁₂

⇒ P = ^{3920 × 100}/₁₁₂

⇒ P = ³⁹²⁰⁰⁰/₁₁₂

⇒ P = $3500

Thus, the sum borrowed (P) = $3500 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 12

Thus, simple interest for 3 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 3920, then the Principal = ¹⁰⁰/₁₁₂ × 3920

= ^{100 × 3920}/₁₁₂

= ³⁹²⁰⁰⁰/₁₁₂

= 3500

Thus, Principal = $3500

Thus, the sum borrowed = $3500 Answer

Similar Questions

(1) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 5% simple interest?

(2) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.

(3) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?

(4) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?

(5) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?

(6) How much loan did Charles borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6785 to clear it?

(7) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.

(8) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 9% simple interest?

(9) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 4% simple interest?

(10) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.