Question

- You are about to deposit $569 into one of the following savings accounts to be left on deposit for 25 years. Each bank offers an account with a different interest rate and compounding period. Assuming you want to maximize your wealth, how much money would be in the bank account that offers the best effective rate of return after 25 years?

Bank A: 9.5 percent rate compounded semi-annually

Bank B: 9.4 percent rate compounded monthly

Bank C: 9.3 percent rate compounded daily

Bank D: 9.2 percent rate compounded continuously

Answer #1

Ans- calculation of effective interest rates:-

Formula E= (1+I/n)^{n} - 1

Bank A - 9.5% compounding semi annually

E =[ (1+0.095/2)^{2} -1]× 100 = 9.726%

Bank B -9.4% compounding montly

E= [(1+0.094/12)^{12} - 1] × 100. = 9.816%

Bank C - 9.3% compounding daily

E= [(1+0.093/365)^{365} -1]× 100 = 9.745%

Bank D = 9.2% compounding continuously

Formula for this E = e^{i} - 1

= e^{0.092} - 1

= 0.09636 . = 9.636%

Calculation of amount in bank after 25 years on the basis of best effective rate of return:

The best effective rate of return is 9.816 i.e, montly compounding i.e, BANK B-

Amount in bank account after 25 years in bank B:-

Amount = P(1+E)^{n}

^{ } = 569(1+0.09816)^{25
} = $5912.25

The money would be in the bank account that offers the best effective rate of return i.e, bank B after 25 years is 5912.25

1. If a bank advertises a savings account that pays a 6% nominal
interest rate compounded continuously, what is the effective annual
percentage rate?
2. Bank A offers a nominal annual interest rate of 5% compounded
daily, while Bank B offers continuous compounding at a 4.6% nominal
annual rate. If you deposit $3,000 with each bank, what will be the
difference in the two bank account balances after two years?
(Show ALL work and formulas used!)

You have $2,500 to deposit into a savings account. The five
banks in your area offer the following rates. In which bank should
you deposit your savings?
Bank B: 3.69%, compounded monthly
Bank A: 3.75%, compounded annually
Bank E; 3.65% compounded quarterly
Bank D: 3.67% compounded continuously
Bank C: 3.70% compounded semi-annually

You plan to deposit $5,500 into a savings account. There are
five great banks in your town offering terrific interest rates. If
your goal is to earn the greatest amount of interest, which bank
should you choose?
Bank DEF: 3.70%, compounded monthly
Bank ABC: 3.74%, compounded annually
Bank HIJ: 3.71% compounded semi-annually
Bank XYZ; 3.64% compounded quarterly
Bank KLM: 3.66% compounded continuously

You have $5,000 that you want to use to open a savings account.
There are five banks located in your area. The rates paid by banks
A through E, respectively, are given below. Which bank should you
select if your goal is to maximize your interest income?
"4.10 percent, compounded continuously"
"4.25 percent, compounded semi-annually"
"4.20 percent, compounded quarterly"
"4.15 percent, compounded monthly"
"4.28 percent, compounded annually"

16. You have $1,000 to deposit in a savings account for 1 year.
You can get a passbook savings
account drawing 7.75% interest compounded continuously, or a
certificate of deposit paying 8%
compounded quarterly, or a savings bond paying 8.25% compounded
annually. Which alternative
should you take?
a. 7.75% compounded continuously
b. 8% compounded quarterly
c. 8.25% compounded annually
d. all of the above are have equal annualized yields
17. You are considering two investments described below:
Investment
A 10%...

1.
A bank offers 6.00% on savings accounts. What is the effective
annual rate if interest is compounded daily?
Answer Format: Percentage Round to: 4 decimal places (Example:
9.2434%
2. A bank offers 9.00% on savings accounts. What is the
effective annual rate if interest is compounded continuously?
Answer Format: Percentage Round to: 4 decimal places

Haywood Bank is offering 1.8 percent compounded daily on its
savings accounts. You deposit $8,000 today. How much will you have
in your account 11 years from now? (please show work i am
confused)

A local bank is offering 9% compounded semi-annually on savings
accounts. If you deposit $1000 today, how much will you
have in 2.5 yrs.
a. 1,240.41
b. 1,295.03
c. 1,246.18
d. 1,166.32
e. 1192.5
A local bank is offering 9% compounded semi-annually on savings
accounts. If you deposit $1000 today, how much will you
have in 2.5 yrs.
a. 1,240.41
b. 1,295.03
c. 1,246.18
d. 1,166.32
e. 1192.5

5A-1
FV CONTINUOUS COMPOUNDING If you receive $15,000 today and can
invest it at a 6% annual rate compounded continuously, what will be
your ending value after 15 years?
5A-2
PV CONTINUOUS COMPOUNDING In 7 years, you are scheduled to
receive money from a trust established for you by your
grandparents. When the trust matures there will be $200,000 in the
account. If the account earns 9% compounded continuously, how much
is in the account today?
5A-3
FV CONTINUOUS COMPOUNDING...

Assume that you deposit $1,000 in a bank account that promises a
fixed rate of interest of 4% per year for 10 years with annual
compounding. You want to know the balance in your account at the
end of 10 years. Assume that you do not make any withdrawals and
that the bank stays solvent for 10 years (and thus can keep its
promise to pay you in 10 years). Across the street, the savings
& loan offers a similar...

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