Simple Interest
Math MCQs

Question :    If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4100

Solution & Explanation

Solution

Given,

Amount (A) = $4920

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

$4920 = P (1 + 5% × 4)

⇒ $4920 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4920 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4920 = P (1 + ²⁰/₁₀₀)

⇒ $4920 = P (^{100 + 20}/₁₀₀)

⇒ $4920 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4920

⇒ P = ⁴⁹²⁰/_¹²⁰/100

⇒ P = 4920 × ¹⁰⁰/₁₂₀

⇒ P = ^{4920 × 100}/₁₂₀

⇒ P = ⁴⁹²⁰⁰⁰/₁₂₀

⇒ P = $4100

Thus, the sum borrowed (P) = $4100 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 4920, then the Principal = ¹⁰⁰/₁₂₀ × 4920

= ^{100 × 4920}/₁₂₀

= ⁴⁹²⁰⁰⁰/₁₂₀

= 4100

Thus, Principal = $4100

Thus, the sum borrowed = $4100 Answer

Similar Questions

(1) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 8% simple interest?

(2) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 5% simple interest.

(3) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 8% simple interest?

(4) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 3% simple interest?

(5) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.

(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 8 years.

(7) How much loan did Joseph borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6555 to clear it?

(8) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.

(9) If Linda paid $3618 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.