Question

You are opening a saving account today by depositing 20,000 today and then plan on depositing an additional 1000 every year. How many deposits will you have to make before the account reaches 40,000 if the account earns 8% a year? show work please

Answer 1

Depositing saving amount today = $ 20,000

thererafter $1000 every year is deposited to have a combined Future value of $40,000

Calculating no of Depsoits:

Where, C= Periodic Payments = $1,000

r = Periodic Interest rate = 0.08

n= no of periods

future Value = $40,000

Invested amount = $20,000

52500 = 32500(1.08)^n

1.6153846 = (1.08)^n

Taking log both sides,

Log(1.6153846 ) = nlog(1.08)

0.208275942 = n(0.033423755)

n = 6.23

So, 6.23 deposits need to be maid.