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) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 9% simple interest?

(2) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8580 to clear it?

(3) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 6% simple interest.

(4) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8145 to clear the loan, then find the time period of the loan.

(5) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 3% simple interest?

(6) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?

(7) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?

(8) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?

(9) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.

(10) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.