Respuesta :
Answer:
At the end of 6 years, the balance in Lee's account is $88,976
Step-by-step explanation:
I am going to call B1 the balance for the first deposit and B2 the balance for the second deposit. The balance is Lee's account at the end of 6 years is B = B1 + B2.
The compound interest formula is given by:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
A: Amount of money(Balance)
P: Principal(Initial deposit)
r: interest rate(as a decimal value)
n: number of times that interest is compounded per unit t
t: time the money is invested or borrowed for.
First step: Balance B1
A = Amount of money(Balance) = B1(value we have to find)
P = $15,300
r = 0.08
n = 2(semiannually means twice a year)
t = 6
[tex]B1 = 15,300(1 + \frac{0.08}{2})^{12}[/tex]
[tex]B1 = 15,300*(1.60)[/tex]
[tex]B1 = 24,496[/tex]
So, from the first balance, Lee has $24,496
Next step: Balance B2
A = B2
P = $40,300
r = 0.08
n = 2
t = 3(from the beginning of year 4 to the end of year 6, so 3 years).
[tex]B2 = 40,300(1 + \frac{0.08}{2})^{6}[/tex]
[tex]B2 = 40,300*(1.26)[/tex]
[tex]B2 = 64,480[/tex]
From the second balance, Lee has $64,480
Final step: Sum of the balances
B = B1 + B2 = 24,496 + 64,480 = $88,976
At the end of 6 years, the balance in Lee's account is $88,976
