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Simple Interest
Math MCQs


Question :    In how much time a principal of $3050 will amount to $3812.5 at a simple interest of 5% per annum?


Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3050

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

Amount (A) = $3812.5

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 = $3812.5 – $3050 = $762.5

Thus, Simple Interest = $762.5

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 × 762.5/3050 × 5

= 76250/15250

= 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) = 5% per annum

Simple Interest = $762.5 (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 = 5% of Principal

= 5% of $3050

= 5/100 × 3050

= 5 × 3050/100

= 15250/100 = 152.5

Thus, simple Interest for 1 year = $152.5

Now,

∵ If the simple Interest is $152.5, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/152.5 years

∴ If the simple Interest is $762.5, then the time = 1/152.5 × 762.5 years

= 1 × 762.5/152.5 years

= 762.5/152.5 = 5 years

Thus, time (T) = 5 years Answer


Similar Questions

(1) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.

(2) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 5% simple interest.

(4) How much loan did Daniel borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6710 to clear it?

(5) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 8 years.

(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 4 years.

(7) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.

(8) If Andrew paid $5568 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(9) If Elizabeth borrowed $3450 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(10) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 4% simple interest?