Taylor invested $650 in an account paying an interest rate of 2.3% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the
nearest tenth of a year, for the value of the account to reach $880?

Step-by-step explanation:

Given that:

Principal = $650

Interest rate, r = 2.3% = 0.023 compounded daily

Time, t it takes for final amount, A to reach $880

Using the relation :

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

n = number of times compounded per period

Hence, n = 365

880 = 650(1 + 0.023/365)^365t

880/650 = 1.0000630^365t

1.3538461 = 1.0000630^365t

Take the log

0.1315692 = 0.0000273596 * 365t

0.1315692 = 0.0099862t

t = 0.1315692 / 0.0099862

t = 13.175101

t = 13.18 years a

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