Simple Interest
Math MCQs

Question :    John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4400

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

Amount (A) = $7568

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 = $7568 – $4400 = $3168

Thus, Simple Interest = $3168

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 × 3168}/_{4400 × 8}

= ³¹⁶⁸⁰⁰/₃₅₂₀₀

= 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) = $4400

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

Simple Interest = $3168 (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 $4400

= ⁸/₁₀₀ × 4400

= ^{8 × 4400}/₁₀₀

= ³⁵²⁰⁰/₁₀₀ = 352

Thus, simple Interest for 1 year = $352

Now,

∵ If the simple Interest is $352, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₅₂ years

∴ If the simple Interest is $3168, then the time = ¹/₃₅₂ × 3168 years

= ^{1 × 3168}/₃₅₂ years

= ³¹⁶⁸/₃₅₂ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?

(2) How much loan did Patricia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6437.5 to clear it?

(3) In how much time a principal of $3000 will amount to $3300 at a simple interest of 2% per annum?

(4) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 4% simple interest?

(5) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?

(6) Mark had to pay $4928 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 9% simple interest?

(8) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 7% simple interest?

(9) How much loan did Susan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6780 to clear it?

(10) In how much time a principal of $3000 will amount to $3360 at a simple interest of 4% per annum?