Simple Interest
MCQs Math


Question:     Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.


Correct Answer  10

Solution And Explanation

Solution

Given,

Principal (P) = $4300

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

Amount (A) = $7310

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 = $7310 – $4300 = $3010

Thus, Simple Interest = $3010

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 × 3010/4300 × 7

= 301000/30100

= 10 years (using formula)

Thus, Time (T) = 10 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) = $4300

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

Simple Interest = $3010 (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 $4300

= 7/100 × 4300

= 7 × 4300/100

= 30100/100 = 301

Thus, simple Interest for 1 year = $301

Now,

∵ If the simple Interest is $301, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/301 years

∴ If the simple Interest is $3010, then the time = 1/301 × 3010 years

= 1 × 3010/301 years

= 3010/301 = 10 years

Thus, time (T) = 10 years Answer


Similar Questions

(1) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 7 years.

(2) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 7% simple interest?

(3) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.

(4) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9685 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 7 years.

(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 8 years.

(7) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.

(8) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.

(9) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?

(10) In how much time a principal of $3100 will amount to $3472 at a simple interest of 4% per annum?


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