Question

1) You have just paid your subscription to Investing Wisely Weekly through the end of this year. You plan to subscribe to the magazine for the rest of your life. You have two options. You can either renew the subscription annually by paying $85 at the end of each year or you can get a lifetime subscription for $620 payable immediately. Assuming that you can earn 6.0% on your funds and that the annual renewal rate will remain constant, how many years (include at least 2 decimals if necessary) must you live to make the lifetime subscription the better buy?

2) You agree to make 24 deposits of $500 at the end of each month into a bank account. At the end of the 24th month, you will have $13,000 in your account. If the bank compounds interest monthly, what nominal annual interest rate will you be earning?

For number two I have tried using excel and following other answers on here but none are working. I don't need to do it on excel, all I need is to see how the work is done.

Answer 1

1) Life time subscription =620
Annual Subscription at end of each year =85
Rate =6%
For number of years to make lifetime subscription better.
PV of Annual Subscription using annuity method =PV of Lifetime subscription
PMT*((1-(1+r)^-n)/r) =Life time subscription
85*((1-(1+6%)^-n)/6% =620
1-1.06^-n =620*6%/85=0.4376471
1.06^-n =1-0.4376471=0.5623529
Applying log on both sides
-n*log1.06 =log(0.5623529)
n =-log(0.5623529)/log(1.06) =9.88 years

2)Number of periods =24
PMT =500(at end of month)
FV in the account =13000
For calculating rate using financial calculator
N=24;PMT=500;FV=-13000;CPT I/Y =0.6886%
APR or nominal rate =12*0.6886% =8.26%