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David has a savings account with a 5,000 balance today
David has a savings account with a 5,000 balance today. The account earns an annual percentage rate of interest of 1.25%, compounded monthly. David plans to make no other deposits or withdrawals. How many years will it take David's account balance to double?
Expert Solution
Balance in savings account, P = 5,000
Annual interest rate, r = 1.25%
Number of compounding per year, n = 12
Number of years, t = ?
Using the formula,
Amount = P(1+r/n)tn
10,000 = 5,000(1+0.0125/12)12t
10,000/5,000 = (1.0010417)12t
2 = (1.01257)t
Introducing log into the above equation, we get
log 2 = log(1.01257)t
log 2 = t log 1.01257
t = log 2/log 1.01257 = 55.481
It will take 55.481 years to double (10,000) the balance 5,000 in David's savings account.
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