SOLUTION: Hello, the questions is: A bank pays 12% per annum on its savings accounts. At the end of every three years, a 2% bonus is paid on the balance at that time. Find the annual effec

Question 1137008: Hello, the questions is:
A bank pays 12% per annum on its savings accounts. At the end of every three years, a 2% bonus is paid on the balance at that time. Find the annual effective rate of interest earned by an investor if the deposit is withdraw in (a) 3 years (b) 4 years.
I started by noting that j1=12%=.12 and so to find the effective rate I made an equation, letting 1$ accumulate, and tried using .
I am very confused how to integrate the 2% bonus into the problem.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A bank pays 12% per annum on its savings accounts.
At the end of every three years, a 2% bonus is paid on the balance at that time. Find the annual effective rate of interest earned by an investor if the deposit is withdrawn
:
(a) 3 yrs
Let just use $100 and find the accumulated amt after 3 yrs,
annual, so it's pretty simple
A = 100(1+.12)^3
A = 100*1.4049
A = $140.49
With the 2% bonus: 140.49 * 1.02 = 143.30
:
Use this to find the effective interest rate (r)
100*(1+r)^3 = 143.30
(1+r)^3 = 143.30/100
(1+r)^3 = 1.433
Using common logs
log((1+r)^3) = log(1.433)
log equiv of exponents. find the log of 1.433
3*log(1+r) = .156246
log(1+r) = .156246/3
log(1+r) = .05208
Find the antilog of both sides
1 + r = 1.1274
r = 1.1274 - 1
r = .1274 or 12.74% is the effective rate after 3 years with the bonus
:
(b) 4 years. Essentially the same procedure
One more year with the accumulate amt of 143.30 at 12%
1.12(143.30) = $160.49 after 4 yrs, find the new r with this amt
100(1+r)^4 = 160.49
(1+r)^4 = 160.49/100
log((1+r)^4) = log(1.6049)
log(1+r) = .20544/4
log(1+r) = .05136
Antilog
1 + r = 1.1255
r = .1255 or 12.55% is effective rate after 4 yrs
;
Hey, did this make sense to you, should I have been more step-by-step in the 2nd part? CK
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