Simple Interest
Math MCQs

Question :    How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?

Correct Answer  $6700

Solution & Explanation

Solution

Given,

Amount (A) = $7370

Rate of Simple Interest (R) = 2%

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

$7370 = P (1 + 2% × 5)

⇒ $7370 = P (1 + ²/₁₀₀ × 5)

⇒ $7370 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7370 = P (1 + ¹⁰/₁₀₀)

⇒ $7370 = P (^{100 + 10}/₁₀₀)

⇒ $7370 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7370

⇒ P = ⁷³⁷⁰/_¹¹⁰/100

⇒ P = 7370 × ¹⁰⁰/₁₁₀

⇒ P = ^{7370 × 100}/₁₁₀

⇒ P = ⁷³⁷⁰⁰⁰/₁₁₀

⇒ P = $6700

Thus, the sum borrowed (P) = $6700 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 = 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 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 7370, then the Principal = ¹⁰⁰/₁₁₀ × 7370

= ^{100 × 7370}/₁₁₀

= ⁷³⁷⁰⁰⁰/₁₁₀

= 6700

Thus, Principal = $6700

Thus, the sum borrowed = $6700 Answer

Similar Questions

(1) Donna had to pay $5577.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 7 years.

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

(5) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.

(6) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.

(7) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 8 years.

(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.

(10) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.