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) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 7 years.

(2) How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?

(3) John had to pay $3680 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 3% simple interest?

(5) In how much time a principal of $3000 will amount to $3300 at a simple interest of 5% per annum?

(6) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 4 years.

(8) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 4 years.

(9) How much loan did Michelle borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7645 to clear it?

(10) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 4 years.