Sue and Joe each have P60,000 a month to spend on housing and on investments in
ID: 3108489 • Letter: S
Question
Sue and Joe each have P60,000 a month to spend on housing and on investments in mutual fund. Each one decides to purchase a property worth P7,000,000. Sue gets a 30-year loan at an annual rate of 6.625% compounded monthly. Joe gets a 15-year loan at an annual rate of 6.25 percentage compounded monthly. Whatever is left of the P60,000 after the monthly payment for loan is invested monthly in mutual fund. The return on the mutual fund is based on nominal annual interest rate, which, when compounded monthly, gives an effective annual rate of 10 percentage? What is Sue's monthly payment? If Sue invest whatever is left of her P60,000 each month after the monthly payment in a mutual fund, how much money will she have in the fund at the end of 30 years? What is Joe's monthly payment? It seems that Joe has nothing left to invest until his loan is paid off in 15 years. If he then invests the entire P60,000 monthly in a mutual fund in the next 15 years, how much money will he have at the end of 30 years? Who has more money at the end of 30 years, and by how much?Explanation / Answer
Formula for amortization payment is;
Pmt=P*r/(1-(1+r)^-t)
Formula for future value is ;
Fv=Pmt[(1+r)^-t - 1)/r]
a.
By using the amortization payment formula,
Where P is 7000000, t is 30*12=360 time period, r is .06625/12=.005520833
Pmt= 7000000*.005520833/(1-(1+.005520833)^-360)
Pmt= $44821.76
Sue monthly payment = $44821.76
b.
By using future value formula,
Where Pmt is $60000-$44821.76 = $15178.23 , t is 12*30=360 time period,
r is .10/12= .0083333
Fv= 15178.23[(1+.008333)^360 - 1)/.00833]
= $34319633.78
Sue has $34319633.78 in mutual fund after 30 years.
c.
By using amortization Payment formula,
Where P is 7000000, t is 15*12=180 time period, r is .0625/12=0.005208
Pmt= 7000000*.005208/(1-(1+.005208)^-180)
Pmt= $60018.07
Joe monthly payment = $60018.07
d.
By using future value formula,
Where Pmt is $60000 , t is 12*15=180 time period,
r is .10/12= .0083333
Fv= 60000[(1+.008333)^180 - 1)/.00833]
= $24876263.14
Joe has $24876263.14 in mutual fund after 30(total) years.
e
Sue has more money at the end of 30 years by $34319633.78 - $24876263.14 = $9443370.64
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