Question

1)

A) You have $15,100 in a savings account that has been paying 5.2% interest, compounded weekly. If you made one deposit when you opened the account exactly 8 years ago and made no other deposits after that, how much did you initially deposit in the account? Assume 52 weeks per year.

B) Bank A offers an interest of 4% compounded daily, while bank B offers continuous compounding at 3.87% APR. If you deposit $6,292 with each bank, what will be the difference in the two bank account balances after 4 years? Enter your answer as a positive number.

Answer 1

.1

Value of the initial deposit now =$15,000

Annual interest=5.2%=0.052

Weekly interest=(5.2/52)%=0.1%=0.001

Number of years money getting compounded=8

Number of weeks =8*52=416

Initial Deposit=PV=Future Value(FV)/((1+i)^N)

FV=$15,000

i=Interest rate per week=0.001

N=Number of weeks=416

Initial Deposit=15000/((1+0.001)^416)= $ 9,897.26

Initial Deposit

$ 9,897.26

.2 Bank A:

Annual interest=4%=0.04

Daily interest=0.04/365=0.000109589

Number of days in 4 years=4*365=1460

Future value(FV)=Present Value(PV)*((1+i)^N)

PV=$6,292

i=0.000109589

N=1460

FV=6292*(1.000109589^1460)= $ 7,383.67

Account balance after 4 years in Bank A

$         7,383.67

Bank B:

APR=3.87%=0.0387

Initial Deposit=$6,292

Number of years=4

Future value=6292*(e^(0.0387*4)= $ 7,345.43

Account balance after 4 years in Bank B

$         7,345.43

Bank A will have higher amount.

Difference=(7383.67-7345.43)= $ 38.23

Difference in account balance

$               38.23