SOLUTION: Suppose you have $8000 deposited in an account with interest compounded semiannually. After 8 years, the account has grown to $9300. What is the interest rate on this account? (Rou
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Question 1183163: Suppose you have $8000 deposited in an account with interest compounded semiannually. After 8 years, the account has grown to $9300. What is the interest rate on this account? (Round your answer to the nearest hundredth of a percent) Answer by ikleyn(52798) (Show Source):
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Suppose you have $8000 deposited in an account with interest compounded semiannually.
After 8 years, the account has grown to $9300. What is the interest rate on this account?
(Round your answer to the nearest hundredth of a percent)
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Your starting equation is
9300 =
and your goal is to find the unknown annual interest rate r (as decimal).
You simplify your equation
= ,
1.1625 = .
You take logarithm base 10 from both sides
log(1.1625) = 16*log(1+r/2)
and find
= = 0.004087.
Next, you take exponent of both sides and get
= = 1.009455.
Hence,
r/2 = 1.009455 - 1 = 0.009455; r = 2*0.009455 = 0.01891.
Thus the annual percentage compound rate is 1.89%. ANSWER
Solved.
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To see many other similar (and different) solved problems, look into the lesson
- Problems on discretely compound accounts
in this site, and learn the subject from there.
After reading this lesson, you will tackle such problems on your own without asking for help from outside.
