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) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.

(2) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 7% simple interest?

(3) If Jessica borrowed $3750 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(4) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 4% simple interest?

(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 3 years.

(6) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 3 years.

(8) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(9) In how much time a principal of $3100 will amount to $3596 at a simple interest of 4% per annum?

(10) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 3 years.