Answer:
(a) 5.78%
(b) $10,594.63
(c) 5.95%
Explanation:
You want the annual rate, the 1-year balance, and the effective yield on an account in which $10,000 is deposited, and the value doubles in 12 years.
(a) Annual rate
The compound interest formula is ...
A = Pe^(rt)
where P is the amount invested at annual rate r for t years, and A is the account balance.
Solving for r, we have ...
ln(A/P)/t = r
The account value will have doubled when A/P = 2, so the rate is ...
r = ln(2)/12 ≈ 0.057762 ≈ 5.78%
The annual rate is about 5.78%.
(b) 1-year balance
The balance after 1 year is ...
A = 10000·e^(ln(2)/12·1) = 10000·2^(1/12) = 10594.63
The balance after 1 year will be $10,594.63.
(c) Effective yield
The APR (r) will be ...
A = P(1 +r)^t
10594.63 = 10000(1 +r)¹
r = 10594.63/10000 -1 = 0.059463 ≈ 5.95%
The effective yield is about 5.95%.