Simple Interest
Math MCQs

Question :    If Ashley paid $5460 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4550

Solution & Explanation

Solution

Given,

Amount (A) = $5460

Rate of Simple Interest (R) = 5%

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

$5460 = P (1 + 5% × 4)

⇒ $5460 = P (1 + ⁵/₁₀₀ × 4)

⇒ $5460 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $5460 = P (1 + ²⁰/₁₀₀)

⇒ $5460 = P (^{100 + 20}/₁₀₀)

⇒ $5460 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $5460

⇒ P = ⁵⁴⁶⁰/_¹²⁰/100

⇒ P = 5460 × ¹⁰⁰/₁₂₀

⇒ P = ^{5460 × 100}/₁₂₀

⇒ P = ⁵⁴⁶⁰⁰⁰/₁₂₀

⇒ P = $4550

Thus, the sum borrowed (P) = $4550 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 20

Thus, simple interest for 4 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 5460, then the Principal = ¹⁰⁰/₁₂₀ × 5460

= ^{100 × 5460}/₁₂₀

= ⁵⁴⁶⁰⁰⁰/₁₂₀

= 4550

Thus, Principal = $4550

Thus, the sum borrowed = $4550 Answer

Similar Questions

(1) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.

(3) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.

(4) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 8% simple interest?

(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 4 years.

(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.

(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 3 years.

(8) How much loan did Mark borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7680 to clear it?

(9) If Susan paid $4234 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(10) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 4 years.