Simple Interest
Math MCQs

Question :    If Jessica paid $4350 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3750

Solution & Explanation

Solution

Given,

Amount (A) = $4350

Rate of Simple Interest (R) = 4%

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

$4350 = P (1 + 4% × 4)

⇒ $4350 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4350 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4350 = P (1 + ¹⁶/₁₀₀)

⇒ $4350 = P (^{100 + 16}/₁₀₀)

⇒ $4350 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4350

⇒ P = ⁴³⁵⁰/_¹¹⁶/100

⇒ P = 4350 × ¹⁰⁰/₁₁₆

⇒ P = ^{4350 × 100}/₁₁₆

⇒ P = ⁴³⁵⁰⁰⁰/₁₁₆

⇒ P = $3750

Thus, the sum borrowed (P) = $3750 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 4350, then the Principal = ¹⁰⁰/₁₁₆ × 4350

= ^{100 × 4350}/₁₁₆

= ⁴³⁵⁰⁰⁰/₁₁₆

= 3750

Thus, Principal = $3750

Thus, the sum borrowed = $3750 Answer

Similar Questions

(1) Anthony had to pay $4816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.

(3) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 4% simple interest?

(4) What amount does James have to pay after 6 years if he takes a loan of $3000 at 6% simple interest?

(5) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.

(6) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.

(8) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 2% simple interest?

(9) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 6% simple interest?

(10) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?