Simple Interest
Math MCQs

Question :    How much loan did Anthony borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7875 to clear it?

Correct Answer  $6300

Solution & Explanation

Solution

Given,

Amount (A) = $7875

Rate of Simple Interest (R) = 5%

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

$7875 = P (1 + 5% × 5)

⇒ $7875 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7875 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7875 = P (1 + ²⁵/₁₀₀)

⇒ $7875 = P (^{100 + 25}/₁₀₀)

⇒ $7875 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7875

⇒ P = ⁷⁸⁷⁵/_¹²⁵/100

⇒ P = 7875 × ¹⁰⁰/₁₂₅

⇒ P = ^{7875 × 100}/₁₂₅

⇒ P = ⁷⁸⁷⁵⁰⁰/₁₂₅

⇒ 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 7875, then the Principal = ¹⁰⁰/₁₂₅ × 7875

= ^{100 × 7875}/₁₂₅

= ⁷⁸⁷⁵⁰⁰/₁₂₅

= 6300

Thus, Principal = $6300

Thus, the sum borrowed = $6300 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.

(2) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $8344 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 3 years.

(4) If Donna paid $5432 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) What amount does John have to pay after 5 years if he takes a loan of $3200 at 8% simple interest?

(6) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 7% simple interest?

(7) How much loan did Patricia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5922.5 to clear it?

(8) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.

(9) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.

(10) If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.