Simple Interest
Math MCQs

Question :    In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?

Correct Answer  4

Solution & Explanation

Solution

Given,

Principal (P) = $3200

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

Amount (A) = $3584

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 = $3584 – $3200 = $384

Thus, Simple Interest = $384

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 × 384}/_{3200 × 3}

= ³⁸⁴⁰⁰/₉₆₀₀

= 4 years (using formula)

Thus, Time (T) = 4 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) = 3% per annum

Simple Interest = $384 (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 $3200

= ³/₁₀₀ × 3200

= ^{3 × 3200}/₁₀₀

= ⁹⁶⁰⁰/₁₀₀ = 96

Thus, simple Interest for 1 year = $96

Now,

∵ If the simple Interest is $96, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₉₆ years

∴ If the simple Interest is $384, then the time = ¹/₉₆ × 384 years

= ^{1 × 384}/₉₆ years

= ³⁸⁴/₉₆ = 4 years

Thus, time (T) = 4 years Answer

Similar Questions

(1) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 10% simple interest?

(2) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 4 years.

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

(4) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 3% simple interest?

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

(6) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 9% simple interest?

(7) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 4% simple interest?

(8) How much loan did Patricia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5922.5 to clear it?

(9) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.

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