Non Annual Compounding It is now January 1. You plan to make a total of 5 deposi
ID: 2650665 • Letter: N
Question
Non Annual Compounding
It is now January 1. You plan to make a total of 5 deposits of $600 each, one every 6 months, with the first payment being made today. The bank pays a nominal interest rate of 10% but uses semiannual compounding. You plan to leave the money in the bank for 10 years. How much will be in your account after 10 years? Round your answer to the nearest cent.
$
You must make a payment of $1,751.87 in 10 years. To get the money for this payment, you will make 5 equal deposits, beginning today and for the following 4 quarters, in a bank that pays a nominal interest rate of 8% with quarterly compounding. How large must each of the 5 payments be? Round your answer to the nearest cent.
$
Explanation / Answer
a)Number of deposit (n) =5
Semiannual (every 6 month) = 600
interest rate = 10% (semiannual 5%)
Present value of annuity =?
Future value = PMT*[{(1+i)^N-1}/n](1+i)
= 600*[{(1+.05)^5-1}/.05](1+.05)
= 600[{1.2763-1}/.05](1.05)
= 600[5.5256](1.05)
= 34481.38
Now remaining period is 15 period (10*2 - 5 ) so we calculate
the future value of this 3481.38 for remaining period
FV=PV(1+i)^n
= 3481.38(1+.05)^15
= 3481.38*2.0789
= 7237.54
b)now we will make reverse working.in this part as compare to above
Future value at end of 10 year =1751.87
n=35 period (quarterly compounding , in 10 year there are 40 quarter (10*4))
Quarterly rate = 8/4 = 2%
PMT =?,PV=?
PV= FV(1+i)^n
= 1751.87/(1+.02)^35
= 1751.87/2 = 857.935
now we calculate the payment .here n=5 period ,i = 2% PV=?
FV=857.935
PMT=?
FVA=PMT [{(1+i)^n-1}i](1+i)
857.935 = PMT [{(1+.02)^5-1}/.02](1+.02)
857.935 = PMT [(1.1041-1)/.02](1.02)
857.935=PMT [5.2040](1.02)
PMT = 857.935/5.2040*1.02
PMT= 161.63
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