If an initial principal P is invested at an annual rate r and the interest is co
ID: 2896163 • Letter: I
Question
If an initial principal P is invested at an annual rate r and the interest is compounded n times per year, the amount A in the account after t years is A = P(1 + r/n) nt .
1. Jeff's bank offers a 36-month Certificate of Deposit (CD) with an APR of 2.75%.
If P = 2000 what is A(8)?
2. Jeff's bank offers a 36-month Certificate of Deposit (CD) with an APR of 2.5%.
If the principal is 3500, solve the equation A(t) = 4100 for t. (Round your answer to two decimal places.)
t = yr
3. Jeff's bank offers a 24-month Certificate of Deposit (CD) with an APR of 2.75%.
What principal P should be invested so that the account balance is $3500 in two years? (Assume the interest is compounded monthly. Round your answer to two decimal places.)
Explanation / Answer
A = P(1 + r/n) nt
1. r = 2.75%
P =2000
n= 3 years
A(8) = 2000(1 + 0.0275/3) 8*3 = 2000*1.244 = 2489.65
2. P = 3500
r = 2.5%
A(t) = 4100
n = 3
4100 = 3500(1+0.025/3)3t
4100/3500 = (1+0.025/3)3t
1.17 = (1+0.025/3)3t
log 1.17 = 3t log(1.0083)
log(1.17/1.0083) = 3t
3t = 0.064
t = 0.02 year
3. P=?
A = 3500
r = 2.75%
n=2
t =2
3500 = P(1+0.0275/2)4
3500 = P(1.06)
P= 3500/1.06 = 3313.94$