Question

Payments of $500.00 are made at the beginning of each month for four years. The interest
rate is 4.5% compounded monthly. If no further deposits are made.
a) Payments of $500.00 are made at the beginning of each month for four years. The
interest rate is 4.5% compounded monthly. If no further deposits are made, calculate
the accumulated value twelve years after the first deposit.
b) Calculate the amount deposited.
c) Calculate the interest.

Answer 1

Solution-

(a)

According to question,

Payments of $500.00 are made at the beginning of each month for four years with interest rate is 4.5% compounded monthly.

We know that the final value of period payment is

  ........(1)

Here,

P = Period payment = $500

r =rate of interest = 4.5% = 0.045

t =time in years = 4

n = times Compounded = 12 (compounded monthly)

On putting these values in equation (1), we get

Final value after 4 years in dollars is

Now, after 4 years,

time for which money is interest is 12 -4 = 8 yerars

If no further deposits are made, Then the above calculated value act as fixed deposit.

Since the formula for final amount for fixed deposit is

.....(2)

Here,

P' = fixed deposit =$ 26,241.91699

r = interest rate = 4.5% = 0.045

n = 12 (Compounded monthly)

t =time in years = 12 - 4 = 8 years

Putting the values in equation (2), we get

A ≈ $ 37,588

So, the accumulated value twelve years after the first deposit is approximately $ 37,588.

Hence, final value after 12 years is $ 37,588.

(b)

The amount deposited is

=$ (4×12×500) =$ 24,000

(Since $ 500 is deposited for 4 years every month).

Hence, Amount deposited = $24,000.

(c)

The interest earn

= Final amount - amount deposited

= 37,588 - 24,000

=$ 13,588

Hence, interest is $ 13,588.