Simple Interest
Math MCQs

Question :    Daniel had to pay $4592 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  $4100

Solution & Explanation

Solution

Given,

Amount (A) = $4592

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

$4592 = P (1 + 4% × 3)

⇒ $4592 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4592 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $4592 = P (1 + ¹²/₁₀₀)

⇒ $4592 = P (^{100 + 12}/₁₀₀)

⇒ $4592 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4592

⇒ P = ⁴⁵⁹²/_¹¹²/100

⇒ P = 4592 × ¹⁰⁰/₁₁₂

⇒ P = ^{4592 × 100}/₁₁₂

⇒ P = ⁴⁵⁹²⁰⁰/₁₁₂

⇒ P = $4100

Thus, the sum borrowed (P) = $4100 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 4592, then the Principal = ¹⁰⁰/₁₁₂ × 4592

= ^{100 × 4592}/₁₁₂

= ⁴⁵⁹²⁰⁰/₁₁₂

= 4100

Thus, Principal = $4100

Thus, the sum borrowed = $4100 Answer

Similar Questions

(1) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6300 to clear it?

(2) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 3% simple interest?

(3) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.

(4) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 5% simple interest?

(5) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.

(6) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.

(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 8 years.

(8) How much loan did Jacob borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9600 to clear it?

(9) 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.

(10) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.