Simple Interest
Math MCQs

Question :    How much loan did Susan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6215 to clear it?

Correct Answer  $5650

Solution & Explanation

Solution

Given,

Amount (A) = $6215

Rate of Simple Interest (R) = 2%

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

$6215 = P (1 + 2% × 5)

⇒ $6215 = P (1 + ²/₁₀₀ × 5)

⇒ $6215 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6215 = P (1 + ¹⁰/₁₀₀)

⇒ $6215 = P (^{100 + 10}/₁₀₀)

⇒ $6215 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6215

⇒ P = ⁶²¹⁵/_¹¹⁰/100

⇒ P = 6215 × ¹⁰⁰/₁₁₀

⇒ P = ^{6215 × 100}/₁₁₀

⇒ P = ⁶²¹⁵⁰⁰/₁₁₀

⇒ P = $5650

Thus, the sum borrowed (P) = $5650 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 6215, then the Principal = ¹⁰⁰/₁₁₀ × 6215

= ^{100 × 6215}/₁₁₀

= ⁶²¹⁵⁰⁰/₁₁₀

= 5650

Thus, Principal = $5650

Thus, the sum borrowed = $5650 Answer

Similar Questions

(1) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 8 years.

(2) How much loan did Donald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7800 to clear it?

(3) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 7% simple interest?

(4) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.

(6) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 3 years.

(7) In how much time a principal of $3100 will amount to $3875 at a simple interest of 5% per annum?

(8) In how much time a principal of $3200 will amount to $3392 at a simple interest of 2% per annum?

(9) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.

(10) If Christopher borrowed $4000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.