Question

If $3000 is placed in an account at 5% and is compounded quarterly for 5 years. How much is in the account at the end of 5 years? $1200 is placed in an account at 4% compounded annually for 2 years. It is then withdrawn at the end of the two years and placed in another bank at the rate of 5% compounded annually for 4 years. What is the balance in the second account after the 4 years.

Answer 1

If $3000 is placed in an account at 5% compounded quarterly for 5 years. How much is the account at the end of 5 years.

Answer 2

1.

Concept:

Compound interest is the interest on the principal amount and on the interest of the previous years.

Given:

We have,

Principal =  $3000, Rate = 5% and time (x) =  compounded quarterly for 5 years.

Find:

We are asked to find the amount at the end of 5 years​.

Solution:

So,

We have,

Principal (P) =  $3000, Rate (R) = 5% and

time (x) = compounded quarterly for 5 years,

i.e.

x = 5 and n = 4 (As there are 4 quarters in a year)

Now,

For Compound Interest,

When,

Compounded n times a year and after t years, the total amount would be,

i.e.

Amount = P[1 + r/(100*x)]ⁿˣ

So,

Now,

Putting values,

Amount = 3000(1 + 5/(100 * 4)⁴ˣ⁵ = 3000(1 + 0.05/4)²⁰ = $3846.11

So,

The amount at the end of 5 years​ is $3846.11.

Hence, the amount at the end of 5 years​ is $3846.11.

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2.

Concept:

Compound interest is the interest on the principal amount and on the interest of the previous years.

Given:

We have,

Principal =  $1200, Rate = 4% and time (x) =  compounded annualy for 2 years.

Find:

We are asked to find the balance in the second account after the 4 years.

Solution:

So,

We have,

Principal (P) =  $1200, Rate (r) = 4% and time (n) =  compounded annualy for 2 years.

Now,

According to the question,

When Compounded annually for 2 years,

i.e.

Amount = P(1 + r/100)ⁿ

So,

Now,

Putting values,

Amount  =  1200(1 + 4/100)² = 1200(1 + 0.04)² = $1297.92

Now,

When placed in another bank at the rate of 5%  and then compounded annually for 4 years,

Then,

Amount  =  1297.92(1 + 5/100)⁴ = 1200(1 + 0.05)⁴  = $1577.63

So,

The balance in the second account after the 4 years will be $1577.63.

Hence, the balance in the second account after the 4 years will be $1577.63.

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