Problema Solution
Julia wants to earn $5000 interest from her investment of $13 000. How long would she need to wait for this to happen if the interest rate is 4.9% p.a. compounded monthly?
Answer provided by our tutors
P = $13,000
r = 0.049 or 4.9% annual interest rate
t = in years that we need to find
m = 1*12 = 12 compounding periods per year
i = r/m = 0.049/12 interest rate per period
n = t*m = 12t total number of compounding periods
A = 5,000+13,000 = $18,000 the future value
A = P(1 + i)^n
18000 = 13000(1 + 0.049/12)^(12t)
13000(1 + 0.049/12)^(12t) = 18000
(1 + 0.049/12)^(12t) = 18/13
(12t) log (1 + 0.049/12) = log (18/13)
t = (1/12)(log (18/13) / log (1 + 0.049/12))
t = 6.655 years
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she will need to wait approximately 6.655 years.