Problem 1 :
You deposit $3500 into an account that earns 2.5% annual interest. Find the balance after one year if the interest is compounded with the given frequencies:
a. Annually:
b. Quarterly:
c. Monthly:
Solution:
Given, P = $3500, r = 2.5% = 0.025, t = 1
a.
A = P(1 + r/n)^{nt}
Here n = 1
A = 3500(1 + 0.025/1)^{1(1)}
= 3500(1.025)
= $3587.50
b.
A = P(1 + r/n)^{nt}
Here n = 4
A = 3500(1 + 0.025/4)^{4(1)}
= 3500(1.00625)^{4}
= $3588.32
c.
A = P(1 + r/n)^{nt}
Here n = 12
A = 3500(1 + 0.025/12)^{12(1)}
= 3500(1.025)
= $3588.36
Problem 2 :
You deposit $500 into account that earns 1.1% annual interest. Find the balance after three years if the interest is compounded with the given frequencies:
a. Daily:
b. Semiannually:
c. Quarterly:
Solution:
Given, P = $500, r = 1.1% = 0.011, t = 3
a.
A = P(1 + r/n)^{nt}
Here n = 365
A = 500(1 + 0.011/365)^{3(365)}
= $516.78
b.
A = P(1 + r/n)^{nt}
Here n = 2
A = 500(1 + 0.011/2)^{3(2)}
= 500(1.033)
A = $516.73
c.
A = P(1 + r/n)^{nt}
Here n = 4
A = 500(1 + 0.011/4)^{3(4)}
= 500(1.033)
A = $516.75
Problem 3 :
You deposit your PFD worth $878 into a savings account that yields 0.15% (currently the rate for Alaska USA Credit Union's saving account). Suppose the interest is compounded monthly. How much money will be in the account after 4 years if you do not spend any of the money?
Solution:
Given, P = $878, r = 0.15%, t = 4
Problem 4 :
You put $500 on a credit card that charges 15% interest compounded monthly. If you do not make any payments, how will you owe a the end of 1 year?
Solution:
Problem 5 :
Your 3 1/2 year investment of $1.830 with interest of 14% which was compounded quarterly is worth how much after 3 1/2 years?
Solution:
Problem 6 :
You put $1600 on a credit card that charges 15.2% interest compounded monthly. If you make no payments for 6 months, how much will you owe?
Solution:
Problem 7 :
You deposit 50 into an account that yields 3.25% interest compounded weekly. How much money will you have after 1 year? After 10 years?
Solution:
After 1 year:
After 10 years:
Problem 8 :
You invest $5 into an account that yields 2.5% annual interest. How much will you have in your account after 2 years if the account is compounded monthly? Quarterly?
Solution:
Monthly:
Quarterly:
Problem 9 :
You put $1000 into an account that yields 1.5% compounded quarterly. How much will you have after 10 years? Use a calculator to estimate when you will have $500,000.
Solution:
After 10 years:
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