Simple Interest
Math MCQs

Question :    How much loan did Rebecca borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9562.5 to clear it?

Correct Answer  $7650

Solution & Explanation

Solution

Given,

Amount (A) = $9562.5

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

$9562.5 = P (1 + 5% × 5)

⇒ $9562.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9562.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9562.5 = P (1 + ²⁵/₁₀₀)

⇒ $9562.5 = P (^{100 + 25}/₁₀₀)

⇒ $9562.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9562.5

⇒ P = ^9562.5/_¹²⁵/100

⇒ P = 9562.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{9562.5 × 100}/₁₂₅

⇒ P = ⁹⁵⁶²⁵⁰/₁₂₅

⇒ P = $7650

Thus, the sum borrowed (P) = $7650 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 9562.5, then the Principal = ¹⁰⁰/₁₂₅ × 9562.5

= ^{100 × 9562.5}/₁₂₅

= ⁹⁵⁶²⁵⁰/₁₂₅

= 7650

Thus, Principal = $7650

Thus, the sum borrowed = $7650 Answer

Similar Questions

(1) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 4 years.

(2) What amount will be due after 2 years if John borrowed a sum of $3100 at a 10% simple interest?

(3) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 4 years.

(4) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.

(5) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 8% simple interest?

(6) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.

(7) How much loan did Donna borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8220 to clear it?

(8) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.

(9) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7344 to clear the loan, then find the time period of the loan.