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padilas [110]
3 years ago
13

The Monthly Bank pays 3 percent interest, compounded monthly, on their savings accounts. The Daily Bank pays 3 percent interest,

compounded daily, on their savings accounts. You want to have $1,000 saved in an account 2 years from today. The amount you must deposit today in a lump sum to achieve your goal will be:
Mathematics
2 answers:
Nookie1986 [14]3 years ago
8 0

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

Novosadov [1.4K]3 years ago
5 0

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 :

A=p(1+\frac{r}{n})^{nt}

Substituting values in the formula;

1000=p(1+\frac{0.03}{12})^{12\times2}

=> 1000=p(1.0025)^{24}

=> 1000=1.06175p

p=\frac{1000}{1.06175}

p = $941.84

Case 2:

A=$1000

n = 365

t = 2

r = 3% or 0.03

p = ?

1000=p(1+\frac{0.03}{365})^{365\times2}

=> 1000=p(1.0000822)^{730}

=> 1000=1.06184p

p=\frac{1000}{1.06184}

p = $941.76

The amount that we should deposit in each bank is around $942.

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