Isaac invested $460 in an account paying an interest rate of 2.4% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $690?

t = 17 years

Step-by-step explanation:

The formula for interest

A = P (1 + r/n) ^ nt

where a is the amount in the account, p is the principal, r is the rate, n is the number of times compounded per year and t is the time in years

Substituting in what we know

690 = 460 (1+.024/365) ^ 365t

690/460 = (1+.024/365) ^ 365t

1.5 = (1+.024/365) ^ 365t

Taking the log of each side

log (1.5) = 365t log (1+.024/365))

Dividing each side by (1+.024/365)

log (1.5) / log (1+.024/365) = 365t

divide each side by 365

1/365 log (1.5) / log (1+.024/365) = t

t = 16.8949

To the nearest year

t = 17

17 years

Step-by-step explanation:

460 (1 + (2.4/365) %) ^t = 690

1.000065753425^t = 1.5

t ln1.000065753425 = ln1.5

t = 6,166.6535619036 days

6,166.6535619036/365

= 16.8949412655 years