Simple Interest
Math MCQs

Question :    How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?

Correct Answer  $7700

Solution & Explanation

Solution

Given,

Amount (A) = $8470

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

$8470 = P (1 + 2% × 5)

⇒ $8470 = P (1 + ²/₁₀₀ × 5)

⇒ $8470 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8470 = P (1 + ¹⁰/₁₀₀)

⇒ $8470 = P (^{100 + 10}/₁₀₀)

⇒ $8470 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8470

⇒ P = ⁸⁴⁷⁰/_¹¹⁰/100

⇒ P = 8470 × ¹⁰⁰/₁₁₀

⇒ P = ^{8470 × 100}/₁₁₀

⇒ P = ⁸⁴⁷⁰⁰⁰/₁₁₀

⇒ P = $7700

Thus, the sum borrowed (P) = $7700 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 8470, then the Principal = ¹⁰⁰/₁₁₀ × 8470

= ^{100 × 8470}/₁₁₀

= ⁸⁴⁷⁰⁰⁰/₁₁₀

= 7700

Thus, Principal = $7700

Thus, the sum borrowed = $7700 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) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 4 years.

(3) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 7% simple interest?

(4) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.

(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.

(6) If Christopher paid $4480 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

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

(9) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.

(10) In how much time a principal of $3100 will amount to $3596 at a simple interest of 4% per annum?