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Simple Interest
Math MCQs


Question :    Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11946 to clear the loan, then find the time period of the loan.


Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6600

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

Amount (A) = $11946

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 = $11946 – $6600 = $5346

Thus, Simple Interest = $5346

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 × 5346/6600 × 9

= 534600/59400

= 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) = $6600

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

Simple Interest = $5346 (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 $6600

= 9/100 × 6600

= 9 × 6600/100

= 59400/100 = 594

Thus, simple Interest for 1 year = $594

Now,

∵ If the simple Interest is $594, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/594 years

∴ If the simple Interest is $5346, then the time = 1/594 × 5346 years

= 1 × 5346/594 years

= 5346/594 = 9 years

Thus, time (T) = 9 years Answer


Similar Questions

(1) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 7 years.

(2) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.

(3) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.

(4) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 8 years.

(6) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 4% simple interest?

(7) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.

(8) How much loan did Margaret borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7620 to clear it?

(9) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?

(10) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.