Simple Interest
Math MCQs

Question :    How much loan did Dorothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9062.5 to clear it?

Correct Answer  $7250

Solution & Explanation

Solution

Given,

Amount (A) = $9062.5

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

$9062.5 = P (1 + 5% × 5)

⇒ $9062.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9062.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9062.5 = P (1 + ²⁵/₁₀₀)

⇒ $9062.5 = P (^{100 + 25}/₁₀₀)

⇒ $9062.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9062.5

⇒ P = ^9062.5/_¹²⁵/100

⇒ P = 9062.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{9062.5 × 100}/₁₂₅

⇒ P = ⁹⁰⁶²⁵⁰/₁₂₅

⇒ 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 = 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 9062.5, then the Principal = ¹⁰⁰/₁₂₅ × 9062.5

= ^{100 × 9062.5}/₁₂₅

= ⁹⁰⁶²⁵⁰/₁₂₅

= 7250

Thus, Principal = $7250

Thus, the sum borrowed = $7250 Answer

Similar Questions

(1) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 8 years.

(2) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?

(3) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 9% simple interest?

(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 7 years.

(5) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 3 years.

(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 7 years.

(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 3 years.

(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 8 years.

(10) Thomas had to pay $4142 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.