Simple Interest
Math MCQs

Question :    How much loan did Ashley borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8187.5 to clear it?

Correct Answer  $6550

Solution & Explanation

Solution

Given,

Amount (A) = $8187.5

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

$8187.5 = P (1 + 5% × 5)

⇒ $8187.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $8187.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $8187.5 = P (1 + ²⁵/₁₀₀)

⇒ $8187.5 = P (^{100 + 25}/₁₀₀)

⇒ $8187.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $8187.5

⇒ P = ^8187.5/_¹²⁵/100

⇒ P = 8187.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{8187.5 × 100}/₁₂₅

⇒ P = ⁸¹⁸⁷⁵⁰/₁₂₅

⇒ P = $6550

Thus, the sum borrowed (P) = $6550 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 8187.5, then the Principal = ¹⁰⁰/₁₂₅ × 8187.5

= ^{100 × 8187.5}/₁₂₅

= ⁸¹⁸⁷⁵⁰/₁₂₅

= 6550

Thus, Principal = $6550

Thus, the sum borrowed = $6550 Answer

Similar Questions

(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 3 years.

(2) Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 3 years.

(3) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?

(4) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.

(5) If Sandra paid $5162 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.

(7) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9384 to clear the loan, then find the time period of the loan.

(8) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.

(9) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) If Anthony paid $4816 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.