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Simple Interest
Math MCQs


Question :    James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.


Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4000

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $6520

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 = $6520 – $4000 = $2520

Thus, Simple Interest = $2520

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 × 2520/4000 × 7

= 252000/28000

= 9 years (using formula)

Thus, Time (T) = 9 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) = $4000

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $2520 (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 = 7% of Principal

= 7% of $4000

= 7/100 × 4000

= 7 × 4000/100

= 28000/100 = 280

Thus, simple Interest for 1 year = $280

Now,

∵ If the simple Interest is $280, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/280 years

∴ If the simple Interest is $2520, then the time = 1/280 × 2520 years

= 1 × 2520/280 years

= 2520/280 = 9 years

Thus, time (T) = 9 years Answer


Similar Questions

(1) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?

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

(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 7 years.

(4) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.

(5) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 3 years.

(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 7 years.

(7) Christopher took a loan of $6000 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.

(8) How much loan did Emily borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7762.5 to clear it?

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

(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 4 years.