Simple Interest
Math MCQs

Question :    Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $7000

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

Amount (A) = $9520

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 = $9520 – $7000 = $2520

Thus, Simple Interest = $2520

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 × 2520}/_{7000 × 6}

= ²⁵²⁰⁰⁰/₄₂₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $7000

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

Simple Interest = $2520 (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 $7000

= ⁶/₁₀₀ × 7000

= ^{6 × 7000}/₁₀₀

= ⁴²⁰⁰⁰/₁₀₀ = 420

Thus, simple Interest for 1 year = $420

Now,

∵ If the simple Interest is $420, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₂₀ years

∴ If the simple Interest is $2520, then the time = ¹/₄₂₀ × 2520 years

= ^{1 × 2520}/₄₂₀ years

= ²⁵²⁰/₄₂₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 5% simple interest?

(2) How much loan did Amanda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7865 to clear it?

(3) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.

(4) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9512 to clear the loan, then find the time period of the loan.

(5) 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.

(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 8 years.

(7) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 3 years.

(8) 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.

(9) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.

(10) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 8 years.