Simple Interest
Math MCQs

Question :    If Emily paid $5510 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4750

Solution & Explanation

Solution

Given,

Amount (A) = $5510

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

$5510 = P (1 + 4% × 4)

⇒ $5510 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5510 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5510 = P (1 + ¹⁶/₁₀₀)

⇒ $5510 = P (^{100 + 16}/₁₀₀)

⇒ $5510 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5510

⇒ P = ⁵⁵¹⁰/_¹¹⁶/100

⇒ P = 5510 × ¹⁰⁰/₁₁₆

⇒ P = ^{5510 × 100}/₁₁₆

⇒ P = ⁵⁵¹⁰⁰⁰/₁₁₆

⇒ P = $4750

Thus, the sum borrowed (P) = $4750 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 5510, then the Principal = ¹⁰⁰/₁₁₆ × 5510

= ^{100 × 5510}/₁₁₆

= ⁵⁵¹⁰⁰⁰/₁₁₆

= 4750

Thus, Principal = $4750

Thus, the sum borrowed = $4750 Answer

Similar Questions

(1) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 5% simple interest.

(2) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 3 years.

(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 7 years.

(4) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?

(5) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.

(6) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 5% simple interest?

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

(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 7 years.

(9) What amount does James have to pay after 6 years if he takes a loan of $3000 at 6% simple interest?

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