Simple Interest
Math MCQs

Question :    If Daniel paid $4756 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4100

Solution & Explanation

Solution

Given,

Amount (A) = $4756

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

$4756 = P (1 + 4% × 4)

⇒ $4756 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4756 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4756 = P (1 + ¹⁶/₁₀₀)

⇒ $4756 = P (^{100 + 16}/₁₀₀)

⇒ $4756 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4756

⇒ P = ⁴⁷⁵⁶/_¹¹⁶/100

⇒ P = 4756 × ¹⁰⁰/₁₁₆

⇒ P = ^{4756 × 100}/₁₁₆

⇒ P = ⁴⁷⁵⁶⁰⁰/₁₁₆

⇒ 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 = 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 4756, then the Principal = ¹⁰⁰/₁₁₆ × 4756

= ^{100 × 4756}/₁₁₆

= ⁴⁷⁵⁶⁰⁰/₁₁₆

= 4100

Thus, Principal = $4100

Thus, the sum borrowed = $4100 Answer

Similar Questions

(1) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 4% simple interest.

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

(4) What amount does John have to pay after 5 years if he takes a loan of $3200 at 2% simple interest?

(5) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 3 years.

(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.

(7) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $12000 to clear the loan, then find the time period of the loan.

(8) In how much time a principal of $3150 will amount to $3339 at a simple interest of 2% per annum?

(9) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.

(10) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.