Simple Interest
Math MCQs

Question :    How much loan did Rebecca borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9180 to clear it?

Correct Answer  $7650

Solution & Explanation

Solution

Given,

Amount (A) = $9180

Rate of Simple Interest (R) = 4%

Time (T) = 5 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

$9180 = P (1 + 4% × 5)

⇒ $9180 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9180 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9180 = P (1 + ²⁰/₁₀₀)

⇒ $9180 = P (^{100 + 20}/₁₀₀)

⇒ $9180 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9180

⇒ P = ⁹¹⁸⁰/_¹²⁰/100

⇒ P = 9180 × ¹⁰⁰/₁₂₀

⇒ P = ^{9180 × 100}/₁₂₀

⇒ P = ⁹¹⁸⁰⁰⁰/₁₂₀

⇒ P = $7650

Thus, the sum borrowed (P) = $7650 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 = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 4 = 20

Thus, simple interest for 5 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 9180, then the Principal = ¹⁰⁰/₁₂₀ × 9180

= ^{100 × 9180}/₁₂₀

= ⁹¹⁸⁰⁰⁰/₁₂₀

= 7650

Thus, Principal = $7650

Thus, the sum borrowed = $7650 Answer

Similar Questions

(1) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?

(2) In how much time a principal of $3050 will amount to $3416 at a simple interest of 3% per annum?

(3) If Sandra paid $4984 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 8 years.

(5) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 3 years.

(7) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8296 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.

(9) What amount does John have to pay after 5 years if he takes a loan of $3200 at 9% simple interest?

(10) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 4% simple interest?