Simple Interest
Math MCQs

Question :    If Donald paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4500

Solution & Explanation

Solution

Given,

Amount (A) = $5220

Rate of Simple Interest (R) = 4%

Time (T) = 4 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

$5220 = P (1 + 4% × 4)

⇒ $5220 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5220 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5220 = P (1 + ¹⁶/₁₀₀)

⇒ $5220 = P (^{100 + 16}/₁₀₀)

⇒ $5220 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5220

⇒ P = ⁵²²⁰/_¹¹⁶/100

⇒ P = 5220 × ¹⁰⁰/₁₁₆

⇒ P = ^{5220 × 100}/₁₁₆

⇒ P = ⁵²²⁰⁰⁰/₁₁₆

⇒ P = $4500

Thus, the sum borrowed (P) = $4500 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 = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 5220, then the Principal = ¹⁰⁰/₁₁₆ × 5220

= ^{100 × 5220}/₁₁₆

= ⁵²²⁰⁰⁰/₁₁₆

= 4500

Thus, Principal = $4500

Thus, the sum borrowed = $4500 Answer

Similar Questions

(1) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.

(2) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 3 years.

(4) Calculate the amount due if Michael borrowed a sum of $3300 at 4% simple interest for 3 years.

(5) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.

(7) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?

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

(9) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 5% simple interest?

(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 4 years.