Simple Interest
Math MCQs

Question :    If Betty paid $5100 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4250

Solution & Explanation

Solution

Given,

Amount (A) = $5100

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

$5100 = P (1 + 5% × 4)

⇒ $5100 = P (1 + ⁵/₁₀₀ × 4)

⇒ $5100 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $5100 = P (1 + ²⁰/₁₀₀)

⇒ $5100 = P (^{100 + 20}/₁₀₀)

⇒ $5100 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $5100

⇒ P = ⁵¹⁰⁰/_¹²⁰/100

⇒ P = 5100 × ¹⁰⁰/₁₂₀

⇒ P = ^{5100 × 100}/₁₂₀

⇒ P = ⁵¹⁰⁰⁰⁰/₁₂₀

⇒ P = $4250

Thus, the sum borrowed (P) = $4250 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 5100, then the Principal = ¹⁰⁰/₁₂₀ × 5100

= ^{100 × 5100}/₁₂₀

= ⁵¹⁰⁰⁰⁰/₁₂₀

= 4250

Thus, Principal = $4250

Thus, the sum borrowed = $4250 Answer

Similar Questions

(1) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 6% simple interest?

(2) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.

(3) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.

(4) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan.

(5) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9955 to clear the loan, then find the time period of the loan.

(6) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?

(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 8 years.

(8) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 8 years.

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

(10) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.