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) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.

(2) How much loan did Margaret borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7937.5 to clear it?

(3) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.

(4) If Steven paid $5520 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 8 years.

(6) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.

(7) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.

(8) Kenneth had to pay $5300 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 4 years.

(10) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 9% simple interest?