Question

how much more would you need to deposit at end of every month to accumulate $287500 over 18 years if the interest rate earned is 4.5% compounded annually instead of 4.5% compounded monthly?

Answer 1

FVOrdinary Annuity = C*(((1 + i/(f*100))^(n*f) -1)/(i/(f*100)))

C = Cash flow per period

i = interest rate

n = number of payments I f = frequency of payment

287500= Cash Flow*(((1+ 4.5/1200)^(18*12)-1)/(4.5/1200))

Cash Flow = 866.31

Using Calculator: press buttons "2ND"+"FV" then assign

FV =287500

I/Y =4.5/12

N =18*12

PV = 0

CPT PMT

Using Excel

=PMT(rate,nper,pv,fv,type)

=PMT(4.5/(12*100),12*18,,287500,)

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

? = ((1+4.5/(12*100))^12-1)*100

Effective Annual Rate% = 4.594

FVOrdinary Annuity = C*(((1 + i/(f*100))^(n*f) -1)/(i/(f*100)))

C = Cash flow per period

i = interest rate

n = number of payments I f = frequency of payment

287500= Cash Flow*(((1+ 4.594/1200)^(18*12)-1)/(4.594/1200))

Cash Flow = 858.1

Using Calculator: press buttons "2ND"+"FV" then assign

FV =287500

I/Y =4.594/12

N =18*12

PV = 0

CPT PMT

Using Excel

=PMT(rate,nper,pv,fv,type)

=PMT(4.594/(12*100),12*18,,287500,)

Difference = 866.31-858.1

= 8.21