Simple Interest
Math MCQs

Question :    How much loan did Donna borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8562.5 to clear it?

Correct Answer  $6850

Solution & Explanation

Solution

Given,

Amount (A) = $8562.5

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

$8562.5 = P (1 + 5% × 5)

⇒ $8562.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $8562.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $8562.5 = P (1 + ²⁵/₁₀₀)

⇒ $8562.5 = P (^{100 + 25}/₁₀₀)

⇒ $8562.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $8562.5

⇒ P = ^8562.5/_¹²⁵/100

⇒ P = 8562.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{8562.5 × 100}/₁₂₅

⇒ P = ⁸⁵⁶²⁵⁰/₁₂₅

⇒ P = $6850

Thus, the sum borrowed (P) = $6850 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 8562.5, then the Principal = ¹⁰⁰/₁₂₅ × 8562.5

= ^{100 × 8562.5}/₁₂₅

= ⁸⁵⁶²⁵⁰/₁₂₅

= 6850

Thus, Principal = $6850

Thus, the sum borrowed = $6850 Answer

Similar Questions

(1) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 3% simple interest.

(2) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?

(3) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 6% simple interest?

(4) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 8 years.

(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 3 years.

(7) How much loan did Joseph borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6555 to clear it?

(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 8 years.

(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 7 years.

(10) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.