Answer:
a) $1110.20
b) 46.18 years
Step-by-step explanation:
We must apply the exponential formula for the calculation of annual compound interest problems
The formula is:
[tex]P = P_0(1 + r) ^ t[/tex]
Where P is the profit after t years
[tex]P_0[/tex] is the initial investment
r is the interest rate.
So in this problem, we have the quarterly interest rate.
We want to find the balance after 3 years. If in a year there are 4 quarters, then in 3 years there are t = 12 quarters.
a) To find the balance we substitute [tex]P_0 = 1000[/tex], [tex]t = 12[/tex] quarters, [tex]r = \frac{0.035}{4}[/tex]
[tex]P = 1000(1 + \frac{0.035}{4}) ^ {12}\\\\P = \$1110.20[/tex]
b) We must calculate t necessary to make the balance of 5000
[tex]5000 = 1000(1 + \frac{0.035}{4}) ^ {4t}\\\\5 = (1 + \frac{0.035}{4}) ^ {4t}\\\\5 = (1.00875) ^ {4t}\\\\log(5) = 4tlog(1.00875)\\\\t = \frac{log(5)}{4log(1.00875)}\\\\t =\ 46.18 years[/tex]
