Simple Interest
Math MCQs

Question :    If Barbara paid $4260 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3550

Solution & Explanation

Solution

Given,

Amount (A) = $4260

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

$4260 = P (1 + 5% × 4)

⇒ $4260 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4260 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4260 = P (1 + ²⁰/₁₀₀)

⇒ $4260 = P (^{100 + 20}/₁₀₀)

⇒ $4260 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4260

⇒ P = ⁴²⁶⁰/_¹²⁰/100

⇒ P = 4260 × ¹⁰⁰/₁₂₀

⇒ P = ^{4260 × 100}/₁₂₀

⇒ P = ⁴²⁶⁰⁰⁰/₁₂₀

⇒ P = $3550

Thus, the sum borrowed (P) = $3550 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 4260, then the Principal = ¹⁰⁰/₁₂₀ × 4260

= ^{100 × 4260}/₁₂₀

= ⁴²⁶⁰⁰⁰/₁₂₀

= 3550

Thus, Principal = $3550

Thus, the sum borrowed = $3550 Answer

Similar Questions

(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 8 years.

(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 8 years.

(3) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9348 to clear the loan, then find the time period of the loan.

(4) In how much time a principal of $3050 will amount to $3812.5 at a simple interest of 5% per annum?

(5) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.

(6) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7152 to clear the loan, then find the time period of the loan.

(7) If Richard paid $4032 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.

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