Simple Interest
Math MCQs

Question :    How much loan did Melissa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8820 to clear it?

Correct Answer  $7350

Solution & Explanation

Solution

Given,

Amount (A) = $8820

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

$8820 = P (1 + 4% × 5)

⇒ $8820 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8820 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8820 = P (1 + ²⁰/₁₀₀)

⇒ $8820 = P (^{100 + 20}/₁₀₀)

⇒ $8820 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8820

⇒ P = ⁸⁸²⁰/_¹²⁰/100

⇒ P = 8820 × ¹⁰⁰/₁₂₀

⇒ P = ^{8820 × 100}/₁₂₀

⇒ P = ⁸⁸²⁰⁰⁰/₁₂₀

⇒ P = $7350

Thus, the sum borrowed (P) = $7350 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 8820, then the Principal = ¹⁰⁰/₁₂₀ × 8820

= ^{100 × 8820}/₁₂₀

= ⁸⁸²⁰⁰⁰/₁₂₀

= 7350

Thus, Principal = $7350

Thus, the sum borrowed = $7350 Answer

Similar Questions

(1) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 5% simple interest?

(2) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.

(3) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 8 years.

(4) James had to pay $3180 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 5% simple interest?

(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 7 years.

(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 7 years.

(9) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 10% simple interest.