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) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.

(2) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 6% simple interest?

(3) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.

(4) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 3 years.

(6) Steven had to pay $5290 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 8 years.

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

(10) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 3% simple interest?