Simple Interest
Math MCQs

Question :    Sandra had to pay $4717 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $4450

Solution & Explanation

Solution

Given,

Amount (A) = $4717

Rate of Simple Interest (R) = 2%

Time (T) = 3 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

$4717 = P (1 + 2% × 3)

⇒ $4717 = P (1 + ²/₁₀₀ × 3)

⇒ $4717 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $4717 = P (1 + ⁶/₁₀₀)

⇒ $4717 = P (^{100 + 6}/₁₀₀)

⇒ $4717 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $4717

⇒ P = ⁴⁷¹⁷/_¹⁰⁶/100

⇒ P = 4717 × ¹⁰⁰/₁₀₆

⇒ P = ^{4717 × 100}/₁₀₆

⇒ P = ⁴⁷¹⁷⁰⁰/₁₀₆

⇒ P = $4450

Thus, the sum borrowed (P) = $4450 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

Calculation of the Amount

Since, in the question, time = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 4717, then the Principal = ¹⁰⁰/₁₀₆ × 4717

= ^{100 × 4717}/₁₀₆

= ⁴⁷¹⁷⁰⁰/₁₀₆

= 4450

Thus, Principal = $4450

Thus, the sum borrowed = $4450 Answer

Similar Questions

(1) How much loan did Mark borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7040 to clear it?

(2) What amount does William have to pay after 5 years if he takes a loan of $3500 at 3% simple interest?

(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 8 years.

(4) How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?

(5) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 4 years.

(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 7 years.

(8) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 7 years.

(9) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 7% simple interest?

(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 7 years.