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A warden meets with 23 prisoners. He tells them the following:
1 answer:
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Answer:
a,b,c,d,e,f) The effective annual yield is 1.1P-P = 0.1P = 10%P.
Step-by-step explanation:
This is a compound interest problem
Compound interest formula:
The compound interest formula is given by:
A: Amount of money(Balance)
P: Principal(Initial deposit)
r: interest rate(as a decimal value)
n: number of times that interest is compounded per unit t
t: time the money is invested or borrowed for.
a)
r = 0.06
n: 2(semianually means that the interest is compounded twice a year).
t = 1.
The acount started the year with P, and it ended with 1.1P, so the effective annual yield is 1.1P-P = 0.1P = 10%P.
b)
Now we have n = 3, since if the interest is compounded quarterly, is is compounded three times a year(a year has 3 quarters). So:
The effective annual yield is 1.1P-P = 0.1P = 10%P.
c) Now we have n = 12, since the interest is compounded monthly, and there are 12 months a year. So:
The effective annual yield is 1.1P-P = 0.1P = 10%P.
d) Since the interest is compounded daily, and we assume 360 days in a year, n = 360. So:
The effective annual yield is 1.1P-P = 0.1P = 10%P.
e) The interest is compounded 1000 times a year, so n = 1000
The effective annual yield is 1.1P-P = 0.1P = 10%P.
f) The interest is compounded 100000 times a year, so n = 100000
The effective annual yield is 1.1P-P = 0.1P = 10%P.