SOLUTION: 1. Lauren plans to deposit $4,000 into a bank account at the beginning of next month and $100/month into the same account at the end of that month and at the end of each subsequent

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: 1. Lauren plans to deposit $4,000 into a bank account at the beginning of next month and $100/month into the same account at the end of that month and at the end of each subsequent      Log On

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Question 932105: 1. Lauren plans to deposit $4,000 into a bank account at the beginning of next month and $100/month into the same account at the end of that month and at the end of each subsequent month for the next 3 yr. If her bank pays interest at the rate of 5%/year compounded monthly, how much will Lauren have in her account at the end of the 3 yr? (Assume she makes no withdrawals during the 3-yr period.) Please round the answer to the nearest cent.
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2. Pierce Publishing sells encyclopedias under two payment plans: cash or installment. Under the installment plan, the customer pays $21/month over 3 yr with interest charged on the balance at a rate of 15%/year compounded monthly. Find the cash price for a set of encyclopedias if it is equivalent to the price paid by a customer using the installment plan. Please round the answer to the nearest cent.
Answer by ptfile(81) About Me  (Show Source):
You can put this solution on YOUR website!
Let  r = interest rate
     n = number of intervals
     t = duration of the payment
     A = monthly installment 
    PV = Present Value
    FV = Final Value

1.



FV+=+4000%281.156652858%29%2B100%28.161472245%2F.004166667%29
FV+=+4626.611432%2B100%2838.7533357%29
FV+=+4626.611432%2B3875.33357
FV+=+8501.95

Her balance in 3 years is $8501.95.

2.
A+=P%28%28%28r%2Fn%29%281%2Br%2Fn%29%5E%28nt%29%29%2F%28%281%2Br%2Fn%29%5E%28nt%29-1%29%29

21=P%28%28%28.0125%29%281.0125%29%5E36%29%2F%28%281.0125%29%5E36-1%29%29
21=P%28%28.0125%29%281.563943819%29%2F.563943819%29
21=P%28.019549298%2F.563943819%29
21=P%28.034665329%29
605.79+=+P

The price of a set of encyclopedias is $605.79.