Simple Interest
Math MCQs

Question :    How much loan did Jessica borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6325 to clear it?

Correct Answer  $5750

Solution & Explanation

Solution

Given,

Amount (A) = $6325

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

$6325 = P (1 + 2% × 5)

⇒ $6325 = P (1 + ²/₁₀₀ × 5)

⇒ $6325 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6325 = P (1 + ¹⁰/₁₀₀)

⇒ $6325 = P (^{100 + 10}/₁₀₀)

⇒ $6325 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6325

⇒ P = ⁶³²⁵/_¹¹⁰/100

⇒ P = 6325 × ¹⁰⁰/₁₁₀

⇒ P = ^{6325 × 100}/₁₁₀

⇒ P = ⁶³²⁵⁰⁰/₁₁₀

⇒ P = $5750

Thus, the sum borrowed (P) = $5750 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 6325, then the Principal = ¹⁰⁰/₁₁₀ × 6325

= ^{100 × 6325}/₁₁₀

= ⁶³²⁵⁰⁰/₁₁₀

= 5750

Thus, Principal = $5750

Thus, the sum borrowed = $5750 Answer

Similar Questions

(1) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.

(2) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 9% simple interest?

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

(4) How much loan did Ashley borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8187.5 to clear it?

(5) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.

(6) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 6% simple interest?

(7) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 5% simple interest?

(9) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?

(10) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 3 years.