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Simple Interest
Math MCQs


Question :    William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.


Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5000

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $8150

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 = $8150 – $5000 = $3150

Thus, Simple Interest = $3150

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 × 3150/5000 × 9

= 315000/45000

= 7 years (using formula)

Thus, Time (T) = 7 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) = $5000

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $3150 (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 = 9% of Principal

= 9% of $5000

= 9/100 × 5000

= 9 × 5000/100

= 45000/100 = 450

Thus, simple Interest for 1 year = $450

Now,

∵ If the simple Interest is $450, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/450 years

∴ If the simple Interest is $3150, then the time = 1/450 × 3150 years

= 1 × 3150/450 years

= 3150/450 = 7 years

Thus, time (T) = 7 years Answer


Similar Questions

(1) What amount will be due after 2 years if William borrowed a sum of $3250 at a 9% simple interest?

(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.

(3) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.

(4) How much loan did Emily borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8437.5 to clear it?

(5) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.

(6) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.

(7) How much loan did Lisa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6655 to clear it?

(8) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?

(9) In how much time a principal of $3000 will amount to $3480 at a simple interest of 4% per annum?

(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.