Question

Nonannual Compounding

It is now January 1. You plan to make a total of 5 deposits of $400 each, one every 6 months, with the first payment being made today. The bank pays a nominal interest rate of 12% but uses semiannual compounding. You plan to leave the money in the bank for 10 years. Do not round intermediate calculations. Round your answers to the nearest cent.

1. How much will be in your account after 10 years?

   $ ___________

2. You must make a payment of $1,992.04 in 10 years. To get the money for this payment, you will make five equal deposits, beginning today and for the following 4 quarters, in a bank that pays a nominal interest rate of 12% with quarterly compounding. How large must each of the five payments be?

   $ _____________

Answer 1

Answer a) Number of deposit (nper) = 5 deposits

Amount per deposit (pmt) = $400 each

Rate (r) = 12%= 6% (semiannual) payment = beginning of time.

Fund accumulated after 5 deposit i.e after 2 years from today using FV(rate,nper,pmt,[pv],[type]).

FV(6%,5,-400,0,1) = 2390.13

The fund will remain investment till end of 10 years i.e. 8 years from the point with 12% semiannual compounding

FV = 2390.13 * ( 1+ 0.12/2)^ 8*2 = $ 6071.77

Answer b) the back calculation of future value V = $1992.04 till end of 10 year with 12% quaterly compounding

five equal deposits, beginning today and for the following 4 quarters. i.e for 1 years,

Present value of 'V' at 10-1 =9 year time

PV = V / ( 1+r/n)^ t*n

PV = 1992.04/ ( 1+0.03)^36 = $ 687.3184

The fund should be accumulated by 5 equal deposit for every quarter at beginning time , by using

PMT(rate, nper, pv, [fv], [type])

PMT ( 3%,5,0,-687.3184,1) = $125.688 = $125.69