Simple Interest
Math MCQs

Question :    If Charles paid $4680 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3900

Solution & Explanation

Solution

Given,

Amount (A) = $4680

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

$4680 = P (1 + 5% × 4)

⇒ $4680 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4680 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4680 = P (1 + ²⁰/₁₀₀)

⇒ $4680 = P (^{100 + 20}/₁₀₀)

⇒ $4680 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4680

⇒ P = ⁴⁶⁸⁰/_¹²⁰/100

⇒ P = 4680 × ¹⁰⁰/₁₂₀

⇒ P = ^{4680 × 100}/₁₂₀

⇒ P = ⁴⁶⁸⁰⁰⁰/₁₂₀

⇒ P = $3900

Thus, the sum borrowed (P) = $3900 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 4680, then the Principal = ¹⁰⁰/₁₂₀ × 4680

= ^{100 × 4680}/₁₂₀

= ⁴⁶⁸⁰⁰⁰/₁₂₀

= 3900

Thus, Principal = $3900

Thus, the sum borrowed = $3900 Answer

Similar Questions

(1) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.

(2) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.

(3) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $8976 to clear the loan, then find the time period of the loan.

(4) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?

(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 8 years.

(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 8 years.

(7) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if William borrowed a sum of $3250 at a 6% simple interest?

(9) If Susan borrowed $3650 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 8 years.