Simple Interest
Math MCQs

Question :    How much loan did Stephanie borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9060 to clear it?

Correct Answer  $7550

Solution & Explanation

Solution

Given,

Amount (A) = $9060

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

$9060 = P (1 + 4% × 5)

⇒ $9060 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9060 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9060 = P (1 + ²⁰/₁₀₀)

⇒ $9060 = P (^{100 + 20}/₁₀₀)

⇒ $9060 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9060

⇒ P = ⁹⁰⁶⁰/_¹²⁰/100

⇒ P = 9060 × ¹⁰⁰/₁₂₀

⇒ P = ^{9060 × 100}/₁₂₀

⇒ P = ⁹⁰⁶⁰⁰⁰/₁₂₀

⇒ P = $7550

Thus, the sum borrowed (P) = $7550 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 9060, then the Principal = ¹⁰⁰/₁₂₀ × 9060

= ^{100 × 9060}/₁₂₀

= ⁹⁰⁶⁰⁰⁰/₁₂₀

= 7550

Thus, Principal = $7550

Thus, the sum borrowed = $7550 Answer

Similar Questions

(1) How much loan did Matthew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6820 to clear it?

(2) In how much time a principal of $3000 will amount to $3360 at a simple interest of 4% per annum?

(3) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.

(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 7 years.

(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 4 years.

(6) How much loan did Joshua borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7935 to clear it?

(7) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.

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

(9) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 5% simple interest?

(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 8 years.