Simple Interest
Math MCQs

Question :    Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6100

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $9028

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 = $9028 – $6100 = $2928

Thus, Simple Interest = $2928

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 × 2928}/_{6100 × 6}

= ²⁹²⁸⁰⁰/₃₆₆₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $6100

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2928 (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 = 6% of Principal

= 6% of $6100

= ⁶/₁₀₀ × 6100

= ^{6 × 6100}/₁₀₀

= ³⁶⁶⁰⁰/₁₀₀ = 366

Thus, simple Interest for 1 year = $366

Now,

∵ If the simple Interest is $366, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₆₆ years

∴ If the simple Interest is $2928, then the time = ¹/₃₆₆ × 2928 years

= ^{1 × 2928}/₃₆₆ years

= ²⁹²⁸/₃₆₆ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 3% simple interest?

(2) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.

(4) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 10% simple interest?

(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 7 years.

(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 8 years.

(7) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.

(8) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 9% simple interest?

(9) How much loan did Thomas borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6670 to clear it?

(10) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?