Simple Interest
Math MCQs

Question :    Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5800

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

Amount (A) = $8932

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 = $8932 – $5800 = $3132

Thus, Simple Interest = $3132

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 × 3132}/_{5800 × 6}

= ³¹³²⁰⁰/₃₄₈₀₀

= 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) = $5800

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

Simple Interest = $3132 (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 $5800

= ⁶/₁₀₀ × 5800

= ^{6 × 5800}/₁₀₀

= ³⁴⁸⁰⁰/₁₀₀ = 348

Thus, simple Interest for 1 year = $348

Now,

∵ If the simple Interest is $348, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₄₈ years

∴ If the simple Interest is $3132, then the time = ¹/₃₄₈ × 3132 years

= ^{1 × 3132}/₃₄₈ years

= ³¹³²/₃₄₈ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Sarah had to pay $4081 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) In how much time a principal of $3150 will amount to $3433.5 at a simple interest of 3% per annum?

(3) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.

(4) How much loan did Barbara borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6660 to clear it?

(5) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 4 years.

(7) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 4 years.

(8) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 10% simple interest?

(9) Linda had to pay $3752 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.