Simple Interest
Math MCQs

Question :    How much loan did Dorothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8337.5 to clear it?

Correct Answer  $7250

Solution & Explanation

Solution

Given,

Amount (A) = $8337.5

Rate of Simple Interest (R) = 3%

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

$8337.5 = P (1 + 3% × 5)

⇒ $8337.5 = P (1 + ³/₁₀₀ × 5)

⇒ $8337.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8337.5 = P (1 + ¹⁵/₁₀₀)

⇒ $8337.5 = P (^{100 + 15}/₁₀₀)

⇒ $8337.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8337.5

⇒ P = ^8337.5/_¹¹⁵/100

⇒ P = 8337.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{8337.5 × 100}/₁₁₅

⇒ P = ⁸³³⁷⁵⁰/₁₁₅

⇒ P = $7250

Thus, the sum borrowed (P) = $7250 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 8337.5, then the Principal = ¹⁰⁰/₁₁₅ × 8337.5

= ^{100 × 8337.5}/₁₁₅

= ⁸³³⁷⁵⁰/₁₁₅

= 7250

Thus, Principal = $7250

Thus, the sum borrowed = $7250 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.

(2) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?

(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 7 years.

(4) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.

(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 4 years.

(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 7 years.

(8) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 3 years.

(9) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?

(10) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.