Question

Rebecca deposited $5,338.18 into a savings account with an interest rate of 5.9% compounded twice a year. About how long will it take for the account to be worth $10,000?
15 years, 11 months
32 years, 5 months
10 years, 10 months
11 years, 0 months

Answer 1

Given:
P = $5338.18, principal
r = 5.9% = 0.059, interest rate
n = 2, nuber of compoundings per year
t =  duraton, years
A = $10,000, target value.

Use the formula
$P(1 + \frac{r}{n})^{nt} = A$

That is,
$5338.18(1 + \frac{0.59}{2})^{2t} =10000\\1.0295^{2t}=1.8773$
$t = \frac{1}{2} ( \frac{ln(1.8773)}{ln(1.0295)} )=10.832\, yrs\,=10yrs,\,10\,mo$

Answer: 10years, 10 months