SOLUTION: 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?

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
,
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
RELATED QUESTIONS
You invest money into an account where the interest is compounded continuously. If the... (answered by RAY100)

You invest $2,000 in an account that is compounded annually at an interest rate of 5%.... (answered by josgarithmetic)

The Morenos invest $10,000 in an account that grows to $12,000 in 5 years. What is the... (answered by ewatrrr)

An amount of $1,000 is deposited into a bank account that pays 4% interest compounded... (answered by mananth)

suppose you invest $1500 in an acount paying 4.75% annual interest. what is the account... (answered by solver91311)

if you invest $20,000 at an APR of 3.5% for 20 years, how much money would you have in... (answered by ikleyn)

Answer the following questions, based on an account that earn 2.8% interest, compounded... (answered by ewatrrr)

How much must be placed each month into a retirement account earning 9% compounded... (answered by ikleyn)

A hospital administrator deposits $10,000 into an account that earns 9% annual interest... (answered by Theo)