Question

2,4% compounded yearly

2000 monthly payment

1 000 000 initial payment

40 years

We are still thinking that the price of the apartment is very expensive, we believe we could convince the bank of making payments only once a year, at the end of the year. The interest rate would still be the same 2.4%, how much money have we saved with this action?

a) In the payments for each year?

b) in the total amount paid for the whole period?

c) what is the present value of the savings?

Answer 1

Sol :

In order to find how much money have been save by monthly payment and yearly payment, we have to find the difference between monthly payment and yearly payment option.

Monthly payment = $2,000

Number of years (n) = 40 x 12 = 480 months

Interest rate (r) = 2.4% (compounded annualy) = 2.4%/12 = 0.20% per period

Future value of monthly payment = Monthly payment (1+r)^n-1/r

Future value of monthly payment = 2000 (1+0.002)^480-1/0.002

Future value of monthly payment = $1,609,193.78

Yearly payment = 2000*12 = 24000

Future value of yearly payment = 24000(1+0.24)^40-1/0.24

Future value of yearly payment = $1,582,249.88

Now total money save paying yearly = $1,609,193.78 - $1,582,249.88 = $26,943.90

a) Money saved in payment each year = $26,943.90/40 = $673.60

b) Money saved in the total amount paid for the whole period = $26,943.90

c) Present value of the savings = FV (1 /(1+r)^n

Present value of the savings = 26943.90 (1/(1+0.024)^40

Therefore Present value of the savings = $10,434.27