Compound Interest rate?

Here is a good challenge!

1.) Mathilda Harper just quit smoking. She estimates that she spent $55 per month on cigarettes. She plans to reward herself by puting the money into a savings account each month. The account pays 4.5% interest compounded monthly. How much money will she have collected in 40 years.

2.) A freight-hauling firm estimates that it will need a new forklift in six years. The estimated cost of the vehicle is $40,000. The company sets up a sinking fund that pays 8% compounded semiannually, into which it will make semiannual payments to achieve the goal. Calculate the size of the payments.

abidex... i see you found this question interesting.

This is the formula that Jun Agruda brought as an answer. Thanks to them!

= $55.00 * 危([1 + {4.5%/12}]^12[40])
= $55.00 * 危([1 + {0.045/12}]^480)
= $55.00 * 危([1 + 0.00375]^480)
= $55.00 * 危(1.00375^480)
= $55.00 * 1,346.1799949446
= $74,039.90

= $40,000.00/(危[1.04^12])
= $40,000.00/15.6268376827597
= $2,559.70

1st question:
= $55.00 * 危([1 + {4.5%/12}]^12[40])
= $55.00 * 危([1 + {0.045/12}]^480)
= $55.00 * 危([1 + 0.00375]^480)
= $55.00 * 危(1.00375^480)
= $55.00 * 1,346.1799949446
= $74,039.90

Answer: $74,039.90

2nd question:
= $40,000.00/(危[1.04^12])
= $40,000.00/15.6268376827597
= $2,559.70

Answer: $2,559.70 should be deposited to sinking fund in semi-annual payments for 6 years or 12 periods.

Do you know?
This is a nice way to complete your homework!!...Dah...
What were you thinking??

The compound interest formula is:

A=P(1+i)^n

where:

'A' = Amount after 'n' interest periods.
'P' = Principal, the amount invested at the start.
'i' = the interest rate applying to each period.
'n' = the number of interest periods

Don't know how to do the rest because there isn't an original principle.

Can you please show me how to do them both?