Simple Interest
Math MCQs

Question :    How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?

Correct Answer  $6750

Solution & Explanation

Solution

Given,

Amount (A) = $7425

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

$7425 = P (1 + 2% × 5)

⇒ $7425 = P (1 + ²/₁₀₀ × 5)

⇒ $7425 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7425 = P (1 + ¹⁰/₁₀₀)

⇒ $7425 = P (^{100 + 10}/₁₀₀)

⇒ $7425 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7425

⇒ P = ⁷⁴²⁵/_¹¹⁰/100

⇒ P = 7425 × ¹⁰⁰/₁₁₀

⇒ P = ^{7425 × 100}/₁₁₀

⇒ P = ⁷⁴²⁵⁰⁰/₁₁₀

⇒ P = $6750

Thus, the sum borrowed (P) = $6750 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 7425, then the Principal = ¹⁰⁰/₁₁₀ × 7425

= ^{100 × 7425}/₁₁₀

= ⁷⁴²⁵⁰⁰/₁₁₀

= 6750

Thus, Principal = $6750

Thus, the sum borrowed = $6750 Answer

Similar Questions

(1) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.

(2) If Charles borrowed $3900 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(3) What amount does David have to pay after 5 years if he takes a loan of $3400 at 6% simple interest?

(4) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 9% simple interest?

(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.

(6) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?

(7) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.

(8) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.

(9) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 6% simple interest?

(10) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.