Question 194017: You invest $1,000 into an account where interest is compounded quarterly. If the account is worth $9,000 in 26 years, what is the interest rate?
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! The formula for compounding quarterly is A = P (1+r/n)^nt,,,where = times /yr,,t==yrs
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A = P (1+r/n)^nt
9000 = 1000 (1+r/4)^(4*26)
9 = ( 1 +r/4)^104
ln9 = 104 ln(1+r/4),,,,,,,,remember ln (1+r/n)^104 = 104 ln (1+r/n)
ln9/104 = .02113 = ln(1+r/4)
e^.02113=(1+r/4),,,,,remember e^ln (1+r/4)=(1+r/4)
1.02135 = 1 + r/4
.02135 = r/4
.0854 =r,,,,,,,,,,,,,,,,,8.54%
,
check
9000= 1000 (1+.0854/4)^(4*26) = 9000,,,ok
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