Simple Interest
Math MCQs

Question :    Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4600

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

Amount (A) = $7820

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 = $7820 – $4600 = $3220

Thus, Simple Interest = $3220

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 × 3220}/_{4600 × 7}

= ³²²⁰⁰⁰/₃₂₂₀₀

= 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) = $4600

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

Simple Interest = $3220 (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 $4600

= ⁷/₁₀₀ × 4600

= ^{7 × 4600}/₁₀₀

= ³²²⁰⁰/₁₀₀ = 322

Thus, simple Interest for 1 year = $322

Now,

∵ If the simple Interest is $322, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₂₂ years

∴ If the simple Interest is $3220, then the time = ¹/₃₂₂ × 3220 years

= ^{1 × 3220}/₃₂₂ years

= ³²²⁰/₃₂₂ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) How much loan did Ryan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9480 to clear it?

(2) How much loan did Melissa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8452.5 to clear it?

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

(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 8 years.

(5) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.

(6) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.

(7) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.

(8) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 8% simple interest?

(9) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.

(10) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.