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) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 4 years.

(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.

(4) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 3% simple interest?

(5) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.

(6) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 10% simple interest?

(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 4 years.

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

(9) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 2% simple interest?

(10) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.