Simple Interest
Math MCQs

Question :    How much loan did Linda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6420 to clear it?

Correct Answer  $5350

Solution & Explanation

Solution

Given,

Amount (A) = $6420

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

$6420 = P (1 + 4% × 5)

⇒ $6420 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6420 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6420 = P (1 + ²⁰/₁₀₀)

⇒ $6420 = P (^{100 + 20}/₁₀₀)

⇒ $6420 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6420

⇒ P = ⁶⁴²⁰/_¹²⁰/100

⇒ P = 6420 × ¹⁰⁰/₁₂₀

⇒ P = ^{6420 × 100}/₁₂₀

⇒ P = ⁶⁴²⁰⁰⁰/₁₂₀

⇒ P = $5350

Thus, the sum borrowed (P) = $5350 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 6420, then the Principal = ¹⁰⁰/₁₂₀ × 6420

= ^{100 × 6420}/₁₂₀

= ⁶⁴²⁰⁰⁰/₁₂₀

= 5350

Thus, Principal = $5350

Thus, the sum borrowed = $5350 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.

(2) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 4 years.

(3) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 4 years.

(4) In how much time a principal of $3150 will amount to $3339 at a simple interest of 3% per annum?

(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 4 years.

(6) Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(7) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 3% simple interest?

(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 4 years.

(9) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.

(10) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.