Number of payments. Your grandfather will sell you a piece of beachfront propert

Question

Number of payments. Your grandfather will sell you a piece of beachfront property for ?$62,500

He says the price is firm whenever you can pay him cash. You know your finances will only allow you to save

?$5,600a year and you can make 7% on your investment. If you invest faithfully every year at the end of the? year, how long will it take for you to accumulate the necessary $62,500 future cash for the beachfront? property?

How long will it take for you to accumulate the neccessary $62,500 future cash for the beachfront property?

Explanation / Answer

Let the years required to accumulate necessary amount be n

Future value requried after n years = $62,500

Annual savings = $5,600

Annual unterest rate = r = 7% = 0.07

Future value of annuity = Annuity amount*{(1+r)n-1}/r

$62,500 = $5,600*(1.07n-1)/0.07

1.07n-1 = $62,500*0.07/$5,600 = 0.78125

1.07n = 0.78125 + 1 = 1.78125

n * log 1.07 = log 1.78125

n = log 1.78125/log 1.07 = 0.250725/0.029384

n = 8.53

Hence, it will take approximately 9 years.

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