Simple Interest
Math MCQs

Question :    How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9360 to clear it?

Correct Answer  $7800

Solution & Explanation

Solution

Given,

Amount (A) = $9360

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

$9360 = P (1 + 4% × 5)

⇒ $9360 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9360 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9360 = P (1 + ²⁰/₁₀₀)

⇒ $9360 = P (^{100 + 20}/₁₀₀)

⇒ $9360 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9360

⇒ P = ⁹³⁶⁰/_¹²⁰/100

⇒ P = 9360 × ¹⁰⁰/₁₂₀

⇒ P = ^{9360 × 100}/₁₂₀

⇒ P = ⁹³⁶⁰⁰⁰/₁₂₀

⇒ P = $7800

Thus, the sum borrowed (P) = $7800 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 9360, then the Principal = ¹⁰⁰/₁₂₀ × 9360

= ^{100 × 9360}/₁₂₀

= ⁹³⁶⁰⁰⁰/₁₂₀

= 7800

Thus, Principal = $7800

Thus, the sum borrowed = $7800 Answer

Similar Questions

(1) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.

(2) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 9% simple interest?

(3) Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(4) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 3 years.

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

(7) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(8) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5712 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 8% simple interest.

(10) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 2% simple interest?