Simple Interest
Math MCQs

Question :    In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?

Correct Answer  2

Solution & Explanation

Solution

Given,

Principal (P) = $3050

Rate of Simple Interest (R) = 3% per annum

Amount (A) = $3233

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $3233 – $3050 = $183

Thus, Simple Interest = $183

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 183}/_{3050 × 3}

= ¹⁸³⁰⁰/₉₁₅₀

= 2 years (using formula)

Thus, Time (T) = 2 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $3050

Rate of Simple Interest (R) = 3% per annum

Simple Interest = $183 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 3% of Principal

= 3% of $3050

= ³/₁₀₀ × 3050

= ^{3 × 3050}/₁₀₀

= ⁹¹⁵⁰/₁₀₀ = 91.5

Thus, simple Interest for 1 year = $91.5

Now,

∵ If the simple Interest is $91.5, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/_91.5 years

∴ If the simple Interest is $183, then the time = ¹/_91.5 × 183 years

= ^{1 × 183}/_91.5 years

= ¹⁸³/_91.5 = 2 years

Thus, time (T) = 2 years Answer

Similar Questions

(1) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?

(2) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 3 years.

(3) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11584 to clear the loan, then find the time period of the loan.

(4) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.

(5) Elizabeth had to pay $3760.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(6) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.

(7) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.

(8) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 3 years.

(10) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.