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) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?

(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 4 years.

(3) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?

(4) If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 9% simple interest?

(6) What amount will be due after 2 years if William borrowed a sum of $3250 at a 4% simple interest?

(7) How much loan did Michael borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6095 to clear it?

(8) How much loan did Margaret borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6985 to clear it?

(9) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.

(10) Mary had to pay $3416 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.