Simple Interest
Math MCQs

Question :    How much loan did Sandra borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7095 to clear it?

Correct Answer  $6450

Solution & Explanation

Solution

Given,

Amount (A) = $7095

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

$7095 = P (1 + 2% × 5)

⇒ $7095 = P (1 + ²/₁₀₀ × 5)

⇒ $7095 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7095 = P (1 + ¹⁰/₁₀₀)

⇒ $7095 = P (^{100 + 10}/₁₀₀)

⇒ $7095 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7095

⇒ P = ⁷⁰⁹⁵/_¹¹⁰/100

⇒ P = 7095 × ¹⁰⁰/₁₁₀

⇒ P = ^{7095 × 100}/₁₁₀

⇒ P = ⁷⁰⁹⁵⁰⁰/₁₁₀

⇒ P = $6450

Thus, the sum borrowed (P) = $6450 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 7095, then the Principal = ¹⁰⁰/₁₁₀ × 7095

= ^{100 × 7095}/₁₁₀

= ⁷⁰⁹⁵⁰⁰/₁₁₀

= 6450

Thus, Principal = $6450

Thus, the sum borrowed = $6450 Answer

Similar Questions

(1) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(2) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 2% simple interest?

(3) What amount does David have to pay after 6 years if he takes a loan of $3400 at 2% simple interest?

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

(5) If Donna paid $5820 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.

(8) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 10% simple interest?

(9) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?

(10) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7872 to clear the loan, then find the time period of the loan.