Simple Interest
Math MCQs

Question :    Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6700

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $9916

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 = $9916 – $6700 = $3216

Thus, Simple Interest = $3216

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 × 3216}/_{6700 × 8}

= ³²¹⁶⁰⁰/₅₃₆₀₀

= 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) = $6700

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $3216 (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 = 8% of Principal

= 8% of $6700

= ⁸/₁₀₀ × 6700

= ^{8 × 6700}/₁₀₀

= ⁵³⁶⁰⁰/₁₀₀ = 536

Thus, simple Interest for 1 year = $536

Now,

∵ If the simple Interest is $536, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₃₆ years

∴ If the simple Interest is $3216, then the time = ¹/₅₃₆ × 3216 years

= ^{1 × 3216}/₅₃₆ years

= ³²¹⁶/₅₃₆ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.

(2) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?

(3) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.

(4) Emily had to pay $5320 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?

(6) 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.

(7) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.

(8) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6109 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 3 years.

(10) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.