Simple Interest
Math MCQs

Question :    If Nancy paid $4814 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4150

Solution & Explanation

Solution

Given,

Amount (A) = $4814

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

$4814 = P (1 + 4% × 4)

⇒ $4814 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4814 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4814 = P (1 + ¹⁶/₁₀₀)

⇒ $4814 = P (^{100 + 16}/₁₀₀)

⇒ $4814 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4814

⇒ P = ⁴⁸¹⁴/_¹¹⁶/100

⇒ P = 4814 × ¹⁰⁰/₁₁₆

⇒ P = ^{4814 × 100}/₁₁₆

⇒ P = ⁴⁸¹⁴⁰⁰/₁₁₆

⇒ P = $4150

Thus, the sum borrowed (P) = $4150 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 4814, then the Principal = ¹⁰⁰/₁₁₆ × 4814

= ^{100 × 4814}/₁₁₆

= ⁴⁸¹⁴⁰⁰/₁₁₆

= 4150

Thus, Principal = $4150

Thus, the sum borrowed = $4150 Answer

Similar Questions

(1) How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?

(2) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 3 years.

(3) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 7 years.

(4) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 9% simple interest.

(6) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 7 years.

(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.

(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.

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

(10) Daniel had to pay $4346 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.