Compound Interest: Suppose a certain amount of money is deposited in an account paying 3% annual interest compounded monthly. For each positive integer n . let S n = the amount on deposit at the end of the nth month, and let S 0 be the initial amount deposited. a. Find a recurrence relation for S 0 , S 1 , S 2 , ... , assuming no additional deposits or withdrawals during the year. Justify your answer. b. If S 0 = $ 10 , 000 , find the amount of money on deposit at the end of one year. c. Find the APY for the account.
Compound Interest: Suppose a certain amount of money is deposited in an account paying 3% annual interest compounded monthly. For each positive integer n . let S n = the amount on deposit at the end of the nth month, and let S 0 be the initial amount deposited. a. Find a recurrence relation for S 0 , S 1 , S 2 , ... , assuming no additional deposits or withdrawals during the year. Justify your answer. b. If S 0 = $ 10 , 000 , find the amount of money on deposit at the end of one year. c. Find the APY for the account.
Solution Summary: The author calculates a recurrence relation for S_0, S'1 and S''_'2mathrm.
Compound Interest: Suppose a certain amount of money is deposited in an account paying 3% annual interest compounded monthly. For each positive integer n. let
S
n
=
the amount on deposit at the end of the nth month, and let
S
0
be the initial amount deposited.
a. Find a recurrence relation for
S
0
,
S
1
,
S
2
,
...
,
assuming no additional deposits or withdrawals during the year. Justify your answer. b. If
S
0
=
$
10
,
000
, find the amount of money on deposit at the end of one year. c. Find the APY for the account.
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