Question

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:

Answer 1

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.

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

Answer 2

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

Explanation:

Case 1:

A=$1000

n = 12

t = 2

r = 3% or 0.03

p = ?

The compound interest formula is :

`A=p(1+(r)/(n))^(nt)`

Substituting values in the formula;

`1000=p(1+(0.03)/(12))^(12*2)`

=>
`1000=p(1.0025)^(24)`

=>
`1000=1.06175p`

`p=(1000)/(1.06175)`

p = $941.84

Case 2:

A=$1000

n = 365

t = 2

r = 3% or 0.03

p = ?

`1000=p(1+(0.03)/(365))^(365*2)`

=>
`1000=p(1.0000822)^(730)`

=>
`1000=1.06184p`

`p=(1000)/(1.06184)`

p = $941.76

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