Simple Interest
MCQs Math


Question:     David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.


Correct Answer  9

Solution And Explanation

Solution

Given,

Principal (P) = $4800

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $9120

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 = $9120 – $4800 = $4320

Thus, Simple Interest = $4320

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 × 4320/4800 × 10

= 432000/48000

= 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) = $4800

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $4320 (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 = 10% of Principal

= 10% of $4800

= 10/100 × 4800

= 10 × 4800/100

= 48000/100 = 480

Thus, simple Interest for 1 year = $480

Now,

∵ If the simple Interest is $480, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/480 years

∴ If the simple Interest is $4320, then the time = 1/480 × 4320 years

= 1 × 4320/480 years

= 4320/480 = 9 years

Thus, time (T) = 9 years Answer


Similar Questions

(1) What amount does William have to pay after 6 years if he takes a loan of $3500 at 6% simple interest?

(2) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 8 years.

(3) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?

(4) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 4 years.

(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 7 years.

(6) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 8 years.

(7) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.

(8) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 7% simple interest?

(9) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.

(10) If Christopher borrowed $4000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.


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