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) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 4 years.

(2) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 7 years.

(3) Sandra had to pay $4850.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(4) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?

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

(6) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 3% simple interest.

(7) In how much time a principal of $3150 will amount to $3433.5 at a simple interest of 3% per annum?

(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 7 years.

(9) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 5% simple interest?

(10) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 7% simple interest.