Simple Interest
Math MCQs

Question :    How much loan did Jennifer borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6300 to clear it?

Correct Answer  $5250

Solution & Explanation

Solution

Given,

Amount (A) = $6300

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

$6300 = P (1 + 4% × 5)

⇒ $6300 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6300 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6300 = P (1 + ²⁰/₁₀₀)

⇒ $6300 = P (^{100 + 20}/₁₀₀)

⇒ $6300 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6300

⇒ P = ⁶³⁰⁰/_¹²⁰/100

⇒ P = 6300 × ¹⁰⁰/₁₂₀

⇒ P = ^{6300 × 100}/₁₂₀

⇒ P = ⁶³⁰⁰⁰⁰/₁₂₀

⇒ P = $5250

Thus, the sum borrowed (P) = $5250 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 6300, then the Principal = ¹⁰⁰/₁₂₀ × 6300

= ^{100 × 6300}/₁₂₀

= ⁶³⁰⁰⁰⁰/₁₂₀

= 5250

Thus, Principal = $5250

Thus, the sum borrowed = $5250 Answer

Similar Questions

(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.

(2) How much loan did Timothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8510 to clear it?

(3) James had to pay $3360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 4 years.

(5) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?

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

(7) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?

(8) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.

(10) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 3 years.