Simple Interest
Math MCQs

Question :    How much loan did Anthony borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7560 to clear it?

Correct Answer  $6300

Solution & Explanation

Solution

Given,

Amount (A) = $7560

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

$7560 = P (1 + 4% × 5)

⇒ $7560 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7560 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7560 = P (1 + ²⁰/₁₀₀)

⇒ $7560 = P (^{100 + 20}/₁₀₀)

⇒ $7560 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7560

⇒ P = ⁷⁵⁶⁰/_¹²⁰/100

⇒ P = 7560 × ¹⁰⁰/₁₂₀

⇒ P = ^{7560 × 100}/₁₂₀

⇒ P = ⁷⁵⁶⁰⁰⁰/₁₂₀

⇒ P = $6300

Thus, the sum borrowed (P) = $6300 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 7560, then the Principal = ¹⁰⁰/₁₂₀ × 7560

= ^{100 × 7560}/₁₂₀

= ⁷⁵⁶⁰⁰⁰/₁₂₀

= 6300

Thus, Principal = $6300

Thus, the sum borrowed = $6300 Answer

Similar Questions

(1) In how much time a principal of $3000 will amount to $3450 at a simple interest of 3% per annum?

(2) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 7 years.

(4) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 10% simple interest.

(5) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 6% simple interest?

(6) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.

(7) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.

(8) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.

(9) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?

(10) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 4% simple interest?