I have inherited $40,000. I want to save it for 5 years to make down payment on new home. I get info from two diff banks.
Bank A - 5.78% APR with semi annual compounding. Bank B - 5.75% APR with daily compounding.
Which bank would you use to maximize your return?
For Bank A - I did .0578*2=1.156. 2P/YR 1.156 NOM% shift EFF% = 1.16.
400000PV 5N 1.16 I/YR FV 41173.53.
Bank B - .0575*365=20.99 365P/YR 20.99 NOM% EFF% = 23.35
400000PV 5N 23.35 I/YR FV 40128.11
BANK A seems to be get higher yield if I did these correctly
bank A:
i = .0578/2 = .0289
n = 10
amount = 40000(1.0289)^10 = 53 185.31
bank B
i = .0575/365 = .000157534
n = 1825
amount = 40000(1.000157534)^1825 = 53 322.39
the yield of bank B is greater than A
so I was supposed to divide not multiply for my initial amount and then if I had used those correctly with the NOM% and EFF I should have come up with it correctly? I will try it again. I could swear in my notes he said we had to multiply. Thanks Again
To determine which bank would maximize your return, you need to calculate the future value (FV) for each bank using the given information.
For Bank A with an APR of 5.78% and semi-annual compounding, you correctly calculated the effective interest rate (EFF%) as 1.16. The formula you used (40000 * (1 + EFF%) ^ 5) gives the future value of the investment after 5 years as $41,173.53.
For Bank B with an APR of 5.75% and daily compounding, the first step is to convert the annual interest rate to a daily rate. You did this correctly by dividing the APR by the number of days in a year, which gave you a daily interest rate of 0.01575% or 0.0001575. Next, you need to calculate the effective annual interest rate (EFF%) using the formula (1 + daily rate) ^ 365 - 1. Plugging in the numbers, we get EFF% = 0.0235 or 2.35%. Now, to calculate the future value, you can use the same formula as before: (40000 * (1 + EFF%) ^ 5), which gives the future value as $40,128.11.
Based on your calculations, Bank A would yield a higher return of $41,173.53 compared to Bank B's $40,128.11 after the 5-year period. Therefore, Bank A appears to offer a higher yield for your investment.