A bank pays 6% nominal annual interest, compounded daily. About how long, nearest day, will it take for a deposit of $1000 to reach $1500?

Question

A bank pays 6% nominal annual interest, compounded daily. About how long, nearest day, will it take for a deposit of $1000 to reach $1500?

Answer 1

1500 = 1000(1 + 0.06/365)^365t

Can you solve for t and answer?

Or do you have a question about method?

Answer 2

answer is close to continuous compounding

FV = PVe^rt

1500 = 1000e^.06t

1.5 = e^.06t

take logs to base e

ln1.5 = .06t

t = (ln1.5)/.06 = about 6.76 days

compounded daily may take a little longer, maybe closer to 7 days

1500 = 1000(1+.06/365)^365t, solve for t

1.5 = (1+ 6/36500)^365t, solve for t

about 7 days

Answer 3

1500/1000 = 3/2

log(3/2) = log (1+.06/365)^365t

log(3/2) = 365t * log(1+ (0.06/365)

log(3/2)/log(1+.06/365) = 365t

2466.78213465 = 365t

t is about 6.75 days so you will need 7 days