Simple Interest
Math MCQs

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

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3100

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

Amount (A) = $3565

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 = $3565 – $3100 = $465

Thus, Simple Interest = $465

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 × 465}/_{3100 × 3}

= ⁴⁶⁵⁰⁰/₉₃₀₀

= 5 years (using formula)

Thus, Time (T) = 5 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) = $3100

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

Simple Interest = $465 (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 $3100

= ³/₁₀₀ × 3100

= ^{3 × 3100}/₁₀₀

= ⁹³⁰⁰/₁₀₀ = 93

Thus, simple Interest for 1 year = $93

Now,

∵ If the simple Interest is $93, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₉₃ years

∴ If the simple Interest is $465, then the time = ¹/₉₃ × 465 years

= ^{1 × 465}/₉₃ years

= ⁴⁶⁵/₉₃ = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

(1) How much loan did Melissa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8820 to clear it?

(2) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 9% simple interest?

(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 3 years.

(4) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.

(5) 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?

(6) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9248 to clear the loan, then find the time period of the loan.

(7) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 8 years.

(9) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.

(10) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.