Simple Interest
Math MCQs

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

Correct Answer  3

Solution & Explanation

Solution

Given,

Principal (P) = $3100

Rate of Simple Interest (R) = 5% 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 × 5}

= ⁴⁶⁵⁰⁰/₁₅₅₀₀

= 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) = $3100

Rate of Simple Interest (R) = 5% 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 = 5% of Principal

= 5% of $3100

= ⁵/₁₀₀ × 3100

= ^{5 × 3100}/₁₀₀

= ¹⁵⁵⁰⁰/₁₀₀ = 155

Thus, simple Interest for 1 year = $155

Now,

∵ If the simple Interest is $155, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₅₅ years

∴ If the simple Interest is $465, then the time = ¹/₁₅₅ × 465 years

= ^{1 × 465}/₁₅₅ years

= ⁴⁶⁵/₁₅₅ = 3 years

Thus, time (T) = 3 years Answer

Similar Questions

(1) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $12540 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 9% simple interest for 3 years.

(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.

(4) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7975 to clear it?

(5) Andrew had to pay $5232 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(6) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?

(7) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.

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

(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 4 years.

(10) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 2% simple interest.