Simple Interest
Math MCQs

Question :  ( 1 of 10 )  In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?

Correct Answer  3

Solution & Explanation

Solution

Given,

Principal (P) = $3200

Rate of Simple Interest (R) = 5% per annum

Amount (A) = $3680

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 = $3680 – $3200 = $480

Thus, Simple Interest = $480

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 × 480}/_{3200 × 5}

= ⁴⁸⁰⁰⁰/₁₆₀₀₀

= 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) = $3200

Rate of Simple Interest (R) = 5% per annum

Simple Interest = $480 (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 $3200

= ⁵/₁₀₀ × 3200

= ^{5 × 3200}/₁₀₀

= ¹⁶⁰⁰⁰/₁₀₀ = 160

Thus, simple Interest for 1 year = $160

Now,

∵ If the simple Interest is $160, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₆₀ years

∴ If the simple Interest is $480, then the time = ¹/₁₆₀ × 480 years

= ^{1 × 480}/₁₆₀ years

= ⁴⁸⁰/₁₆₀ = 3 years

Thus, time (T) = 3 years Answer

Similar Questions

(1) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.

(3) 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?

(4) 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.

(5) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 3 years.

(6) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 7 years.

(7) How much loan did George borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8030 to clear it?

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

(9) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 6% simple interest?

(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 8 years.