A client invests €20,000 in a four- year certificate of deposit (CD) that annually pays interest of 3.5%. The annual CD interest payments are automatically reinvested in a separate savings account at a stated annual interest rate of 2% compounded monthly. At maturity, the value of the combined asset is closest to:

PV = $20.000 CHS i = 3,5 N = 1 PMT = 0 FV = $20.700

so at end of each year you will get $700 dollars from this CD

year 1

PV = 700 CHS n = 3*12 = 36 i = 2/12 = 0,166666667 PMT = 0 (ask)FV = $743,25

you have 4 payments of 700 earning 2% per annum, with payments being made at the end of the period, being deposited into an account that starts off at 0.

Since the second account is compounded monthly, it does not earn 2% between payments. If actually earns 2.0184% (i.e. the effective annual rate).

One of the key concepts is that you must always match the interest rate to the period. If you have an annuity with ANNUAL payments, you must use the interest earned IN A YEAR’S TIME. So, while the solution by Paul is otherwise correct, I/Y should be 2.0184%

as Paul said, the thing is I can`t use 2 as i, you would need to convert it to EAR. I wanted to know a method without having to convert it…

like using 36 N something like that…(as its montly wining from the $700, it wouldnt made any win on the first year cuz the first payment wouldnt exist first year (thats why im thinking of 36 N not 48…)

hey
That really simplifies it but I wanted to understand how do you take N=4, since the 700 will be paid at year 1 end which leaves only 3 years until year 4 end.