Simple Interest
Math MCQs

Question :    How much loan did Barbara borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6660 to clear it?

Correct Answer  $5550

Solution & Explanation

Solution

Given,

Amount (A) = $6660

Rate of Simple Interest (R) = 4%

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

$6660 = P (1 + 4% × 5)

⇒ $6660 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6660 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6660 = P (1 + ²⁰/₁₀₀)

⇒ $6660 = P (^{100 + 20}/₁₀₀)

⇒ $6660 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6660

⇒ P = ⁶⁶⁶⁰/_¹²⁰/100

⇒ P = 6660 × ¹⁰⁰/₁₂₀

⇒ P = ^{6660 × 100}/₁₂₀

⇒ P = ⁶⁶⁶⁰⁰⁰/₁₂₀

⇒ P = $5550

Thus, the sum borrowed (P) = $5550 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 6660, then the Principal = ¹⁰⁰/₁₂₀ × 6660

= ^{100 × 6660}/₁₂₀

= ⁶⁶⁶⁰⁰⁰/₁₂₀

= 5550

Thus, Principal = $5550

Thus, the sum borrowed = $5550 Answer

Similar Questions

(1) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.

(2) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.

(3) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 8 years.

(5) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 2% simple interest?

(6) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.

(8) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 2% simple interest?

(9) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?

(10) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 7 years.