Find the Savings in Five Years
Dave Bidini has saved $29,000 for a down payment on a home and plans to save another $5900 at the conclusion of each year for the next five years. He expects to earn 2.70% compounded annually on his savings. How much will he save in five years' time?
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Since we have an initial deposit of $29,000 and thereafter additional deposits are made at the END of the year, we will use two formulae:
1) A = P(1+r/n)^nt
and
2) A = P * (((1 + r/n)^nt - 1) / (r/n))
The 1st formula will be used for the initial amount of $29000 and the 2nd formula will be used for the yearly savings of $5900.
Using the 1st formula we get A1 = 29000(1 + 0.027/1)^5 = $33,132.195
Using the 2nd formula, we get A2 = 5900(((1 + 0.027/1)^5 - 1)/ (0.027/1) = $ 31,136.59
Adding A1 and A2, we get our answer = $64,268.789
1) A = P(1+r/n)^nt
and
2) A = P * (((1 + r/n)^nt - 1) / (r/n))
The 1st formula will be used for the initial amount of $29000 and the 2nd formula will be used for the yearly savings of $5900.
Using the 1st formula we get A1 = 29000(1 + 0.027/1)^5 = $33,132.195
Using the 2nd formula, we get A2 = 5900(((1 + 0.027/1)^5 - 1)/ (0.027/1) = $ 31,136.59
Adding A1 and A2, we get our answer = $64,268.789
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