Answer:
The amount that we should deposit in each bank is around $942.
Step-by-step explanation:
Case 1:
A=$1000
n = 12
t = 2
r = 3% or 0.03
p = ?
The compound interest formula is :
[tex]A=p(1+\frac{r}{n})^{nt}[/tex]
Substituting values in the formula;
[tex]1000=p(1+\frac{0.03}{12})^{12\times2}[/tex]
=> [tex]1000=p(1.0025)^{24}[/tex]
=> [tex]1000=1.06175p[/tex]
[tex]p=\frac{1000}{1.06175}[/tex]
p = $941.84
Case 2:
A=$1000
n = 365
t = 2
r = 3% or 0.03
p = ?
[tex]1000=p(1+\frac{0.03}{365})^{365\times2}[/tex]
=> [tex]1000=p(1.0000822)^{730}[/tex]
=> [tex]1000=1.06184p[/tex]
[tex]p=\frac{1000}{1.06184}[/tex]
p = $941.76
The amount that we should deposit in each bank is around $942.
Answer: The amount you must deposit today is $941.84 into an account with The Monthly Bank and is $999.92 with The Daily Bank.
Step-by-step explanation:
The formula for calculating compound interest is A=P (1+i)^n where A is the actual amount at the end of the investment. P is the principal amount you need to invest. i is the interest rate in decimal form and n is the number of periods for which you can accumulate interest.
Rearranging the formula:
P = A/(1+i)^n
For The Monthly Bank:
P = $1000/(1+0.03/12)^2×12
P = $941.84
For The Daily Bank:
P = $1000/(1+0.03/365)^2×365
P = $999.92
