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 + (r)/(n))^(nt) = A`

That is,

`5338.18(1 + (0.59)/(2))^(2t) =10000\\1.0295^(2t)=1.8773`

`t = (1)/(2) ( (ln(1.8773))/(ln(1.0295)) )=10.832\, yrs\,=10yrs,\,10\,mo`

Answer: 10years, 10 months