Simple Interest
Math MCQs

Question :    In how much time a principal of $3000 will amount to $3270 at a simple interest of 3% per annum?

Correct Answer  3

Solution & Explanation

Solution

Given,

Principal (P) = $3000

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

Amount (A) = $3270

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 = $3270 – $3000 = $270

Thus, Simple Interest = $270

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 × 270}/_{3000 × 3}

= ²⁷⁰⁰⁰/₉₀₀₀

= 3 years (using formula)

Thus, Time (T) = 3 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) = $3000

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

Simple Interest = $270 (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 $3000

= ³/₁₀₀ × 3000

= ^{3 × 3000}/₁₀₀

= ⁹⁰⁰⁰/₁₀₀ = 90

Thus, simple Interest for 1 year = $90

Now,

∵ If the simple Interest is $90, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₉₀ years

∴ If the simple Interest is $270, then the time = ¹/₉₀ × 270 years

= ^{1 × 270}/₉₀ years

= ²⁷⁰/₉₀ = 3 years

Thus, time (T) = 3 years Answer

Similar Questions

(1) Donna had to pay $5141 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 4% simple interest?

(3) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?

(4) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9348 to clear the loan, then find the time period of the loan.

(5) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 3% simple interest?

(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 8 years.

(7) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 6% simple interest?

(9) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(10) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7301 to clear the loan, then find the time period of the loan.