Simple Interest
Math MCQs

Question :    In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3050

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

Amount (A) = $3507.5

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 = $3507.5 – $3050 = $457.5

Thus, Simple Interest = $457.5

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 × 457.5}/_{3050 × 3}

= ⁴⁵⁷⁵⁰/₉₁₅₀

= 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) = $3050

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

Simple Interest = $457.5 (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 $3050

= ³/₁₀₀ × 3050

= ^{3 × 3050}/₁₀₀

= ⁹¹⁵⁰/₁₀₀ = 91.5

Thus, simple Interest for 1 year = $91.5

Now,

∵ If the simple Interest is $91.5, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/_91.5 years

∴ If the simple Interest is $457.5, then the time = ¹/_91.5 × 457.5 years

= ^{1 × 457.5}/_91.5 years

= ^457.5/_91.5 = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 8 years.

(2) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.

(3) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.

(4) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 6% simple interest?

(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 7 years.

(6) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.

(7) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 9% simple interest?

(8) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.

(9) In how much time a principal of $3200 will amount to $3456 at a simple interest of 4% per annum?

(10) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.