Simple Interest
Math MCQs

Question :    How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?

Correct Answer  $6650

Solution & Explanation

Solution

Given,

Amount (A) = $7315

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

$7315 = P (1 + 2% × 5)

⇒ $7315 = P (1 + ²/₁₀₀ × 5)

⇒ $7315 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7315 = P (1 + ¹⁰/₁₀₀)

⇒ $7315 = P (^{100 + 10}/₁₀₀)

⇒ $7315 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7315

⇒ P = ⁷³¹⁵/_¹¹⁰/100

⇒ P = 7315 × ¹⁰⁰/₁₁₀

⇒ P = ^{7315 × 100}/₁₁₀

⇒ P = ⁷³¹⁵⁰⁰/₁₁₀

⇒ P = $6650

Thus, the sum borrowed (P) = $6650 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 7315, then the Principal = ¹⁰⁰/₁₁₀ × 7315

= ^{100 × 7315}/₁₁₀

= ⁷³¹⁵⁰⁰/₁₁₀

= 6650

Thus, Principal = $6650

Thus, the sum borrowed = $6650 Answer

Similar Questions

(1) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.

(2) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.

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

(4) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.

(5) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?

(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 7 years.

(7) What amount does David have to pay after 6 years if he takes a loan of $3400 at 5% simple interest?

(8) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?

(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 8 years.

(10) In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?