Simple Interest
Math MCQs

Question :    If Mary paid $3660 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3050

Solution & Explanation

Solution

Given,

Amount (A) = $3660

Rate of Simple Interest (R) = 5%

Time (T) = 4 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

$3660 = P (1 + 5% × 4)

⇒ $3660 = P (1 + ⁵/₁₀₀ × 4)

⇒ $3660 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $3660 = P (1 + ²⁰/₁₀₀)

⇒ $3660 = P (^{100 + 20}/₁₀₀)

⇒ $3660 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $3660

⇒ P = ³⁶⁶⁰/_¹²⁰/100

⇒ P = 3660 × ¹⁰⁰/₁₂₀

⇒ P = ^{3660 × 100}/₁₂₀

⇒ P = ³⁶⁶⁰⁰⁰/₁₂₀

⇒ P = $3050

Thus, the sum borrowed (P) = $3050 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 = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 5 = 20

Thus, simple interest for 4 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 3660, then the Principal = ¹⁰⁰/₁₂₀ × 3660

= ^{100 × 3660}/₁₂₀

= ³⁶⁶⁰⁰⁰/₁₂₀

= 3050

Thus, Principal = $3050

Thus, the sum borrowed = $3050 Answer

Similar Questions

(1) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 3 years.

(3) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 7% simple interest?

(4) How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?

(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 7 years.

(6) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?

(7) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.

(8) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.

(10) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.