Simple Interest
Math MCQs

Question :    How much loan did Daniel borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6710 to clear it?

Correct Answer  $6100

Solution & Explanation

Solution

Given,

Amount (A) = $6710

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

$6710 = P (1 + 2% × 5)

⇒ $6710 = P (1 + ²/₁₀₀ × 5)

⇒ $6710 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6710 = P (1 + ¹⁰/₁₀₀)

⇒ $6710 = P (^{100 + 10}/₁₀₀)

⇒ $6710 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6710

⇒ P = ⁶⁷¹⁰/_¹¹⁰/100

⇒ P = 6710 × ¹⁰⁰/₁₁₀

⇒ P = ^{6710 × 100}/₁₁₀

⇒ P = ⁶⁷¹⁰⁰⁰/₁₁₀

⇒ P = $6100

Thus, the sum borrowed (P) = $6100 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 6710, then the Principal = ¹⁰⁰/₁₁₀ × 6710

= ^{100 × 6710}/₁₁₀

= ⁶⁷¹⁰⁰⁰/₁₁₀

= 6100

Thus, Principal = $6100

Thus, the sum borrowed = $6100 Answer

Similar Questions

(1) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11222 to clear the loan, then find the time period of the loan.

(2) What amount does William have to pay after 6 years if he takes a loan of $3500 at 4% simple interest?

(3) How much loan did Anthony borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6930 to clear it?

(4) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.

(5) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?

(6) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9955 to clear the loan, then find the time period of the loan.

(7) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.

(8) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 2% simple interest?

(9) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.

(10) In how much time a principal of $3200 will amount to $3392 at a simple interest of 3% per annum?