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

(2) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 9% simple interest?

(3) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 4% simple interest?

(4) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.

(5) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 7% simple interest?

(6) How much loan did Jessica borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7187.5 to clear it?

(7) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.

(8) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 7 years.

(10) Sandra had to pay $5117.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.