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) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.

(2) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.

(3) How much loan did John borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5720 to clear it?

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

(5) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 8 years.

(6) How much loan did Mary borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6312.5 to clear it?

(7) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 8 years.

(8) How much loan did Jacob borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8800 to clear it?

(9) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 4% simple interest?

(10) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.