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Homework answers / question archive / 1) Calculate the value after 20 years of a Retirement Savings Plan that earned 10% compounded quarterly and received deposits of $6,000 at the start of every three months

1) Calculate the value after 20 years of a Retirement Savings Plan that earned 10% compounded quarterly and received deposits of $6,000 at the start of every three months

Finance

1) Calculate the value after 20 years of a Retirement Savings Plan that earned 10% compounded quarterly and received deposits of $6,000 at the start of every three months.

2) A life insurance company will sell a 20-year annuity paying $1600 at the end of each month for $175,000. What annually compounded nominal rate of interest will the annuitant earn?

3) Rusty borrows $1,000,000 for a mortgage with monthly payments over 30 years at a rate of 9.75% per annum interest. What is the monthly payment?

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1) We can calculate the future value by using the following formula in excel:-

=fv(rate,nper,-pmt,pv,type)

Here,

FV = Future value

Rate = 10%/4 = 2.5% (quarterly)

Nper = 20*4 = 80 periods (quarterly)

Pmt = $6,000

PV = $0

Type = 1

Substituting the values in formula:

= fv(2.5%,80,-6000,0,1)

= $1,527,553.68 Or $1,527,554

 

2) We can calculate the nominal rate by using the following formula in excel:-

=rate(nper,pmt,-pv,fv)

Here,

Rate = Nominal rate (monthly)

Nper = 20*12 = 240 periods (monthly)

Pmt = $1,600

PV = $175,000

FV = $0

Substituting the values in formula:

= rate(240,1600,-175000,0)

= 0.769%

Nominal rate = Rate * 12

= 0.769% * 12

= 9.226%

 

3) We can calculate the monthly payments by using the following formula in excel:-

=pmt(rate,nper,-pv,fv)

Here,

Pmt = Monthly payments

Rate = 9.75%/12 = 0.8125% (monthly)

Nper = 30*12 = 360 periods(monthly)

PV = $1,000,000

FV = $0

Substituting the values in formula:

= pmt(0.8125%,360,-1000000,0)

= $8,591.54

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