Simple Interest
Math MCQs

Question :    How much loan did Michelle borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8687.5 to clear it?

Correct Answer  $6950

Solution & Explanation

Solution

Given,

Amount (A) = $8687.5

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

$8687.5 = P (1 + 5% × 5)

⇒ $8687.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $8687.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $8687.5 = P (1 + ²⁵/₁₀₀)

⇒ $8687.5 = P (^{100 + 25}/₁₀₀)

⇒ $8687.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $8687.5

⇒ P = ^8687.5/_¹²⁵/100

⇒ P = 8687.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{8687.5 × 100}/₁₂₅

⇒ P = ⁸⁶⁸⁷⁵⁰/₁₂₅

⇒ P = $6950

Thus, the sum borrowed (P) = $6950 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 8687.5, then the Principal = ¹⁰⁰/₁₂₅ × 8687.5

= ^{100 × 8687.5}/₁₂₅

= ⁸⁶⁸⁷⁵⁰/₁₂₅

= 6950

Thus, Principal = $6950

Thus, the sum borrowed = $6950 Answer

Similar Questions

(1) How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?

(2) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.

(3) Calculate the amount due if Susan borrowed a sum of $3650 at 3% simple interest for 4 years.

(4) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?

(5) Donald had to pay $4770 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 3 years.

(7) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10168 to clear the loan, then find the time period of the loan.

(8) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.

(9) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.

(10) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.