Simple Interest
Math MCQs

Question :    If Donna paid $5626 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4850

Solution & Explanation

Solution

Given,

Amount (A) = $5626

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

$5626 = P (1 + 4% × 4)

⇒ $5626 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5626 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5626 = P (1 + ¹⁶/₁₀₀)

⇒ $5626 = P (^{100 + 16}/₁₀₀)

⇒ $5626 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5626

⇒ P = ⁵⁶²⁶/_¹¹⁶/100

⇒ P = 5626 × ¹⁰⁰/₁₁₆

⇒ P = ^{5626 × 100}/₁₁₆

⇒ P = ⁵⁶²⁶⁰⁰/₁₁₆

⇒ P = $4850

Thus, the sum borrowed (P) = $4850 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 5626, then the Principal = ¹⁰⁰/₁₁₆ × 5626

= ^{100 × 5626}/₁₁₆

= ⁵⁶²⁶⁰⁰/₁₁₆

= 4850

Thus, Principal = $4850

Thus, the sum borrowed = $4850 Answer

Similar Questions

(1) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?

(2) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.

(3) How much loan did Kevin borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8165 to clear it?

(4) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 3% simple interest?

(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.

(6) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 9% simple interest?

(7) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 4 years.

(9) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.

(10) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.