Simple Interest
Math MCQs

Question :    How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?

Correct Answer  $5250

Solution & Explanation

Solution

Given,

Amount (A) = $6562.5

Rate of Simple Interest (R) = 5%

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

$6562.5 = P (1 + 5% × 5)

⇒ $6562.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $6562.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $6562.5 = P (1 + ²⁵/₁₀₀)

⇒ $6562.5 = P (^{100 + 25}/₁₀₀)

⇒ $6562.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $6562.5

⇒ P = ^6562.5/_¹²⁵/100

⇒ P = 6562.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{6562.5 × 100}/₁₂₅

⇒ P = ⁶⁵⁶²⁵⁰/₁₂₅

⇒ P = $5250

Thus, the sum borrowed (P) = $5250 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 6562.5, then the Principal = ¹⁰⁰/₁₂₅ × 6562.5

= ^{100 × 6562.5}/₁₂₅

= ⁶⁵⁶²⁵⁰/₁₂₅

= 5250

Thus, Principal = $5250

Thus, the sum borrowed = $5250 Answer

Similar Questions

(1) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 7 years.

(2) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7450 to clear the loan, then find the time period of the loan.

(3) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7616 to clear the loan, then find the time period of the loan.

(4) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?

(5) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 3 years.

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

(7) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.

(8) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.

(9) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 7% simple interest?

(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 7 years.