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) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.

(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 8 years.

(3) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.

(4) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.

(5) If Karen borrowed $3950 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(6) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 5% simple interest?

(7) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 7% simple interest?

(8) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $14000 to clear the loan, then find the time period of the loan.

(9) James had to pay $3360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 6% simple interest?