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Scorpion4ik [409]
3 years ago
9

Kathy fields wants to buy a condominium selling for $95,000. The bank is requiring 20% down and is charging 9.5% interest for a

25 year loan. determine the amount required down payment and the amount of the monthly payment for the principal and interest.
Business
1 answer:
tatuchka [14]3 years ago
3 0

Answer:

The down payment is 19000 and monthly payment is 664.009

Explanation:

The purchase price of condominium = $95000

Down payment = 20%

Interest charged  = 9.5 %

Time period = 25 years

Down payment amount =  95000 × 20% = 19000

Remaining loan amount = $76000

Below is the calculation of monthly payment:

\text{Present vlaue of annuity} =\frac{A(1-(1+r)^{-n})}{r} \\A = monthy \ installment \\76000 = \frac{A(1-(1+ 0.095/12)^{-25\times 12})}{ 0.095/12} \\A(0.906112) = 601.667 \\A = 664.009

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The present Value of the growing annuity= $1,158,092.68  

Explanation:

The present value of the growing annuity is going to be computed as follows:

PV = A/(r-g) × (1- (1+g/1+r)^n)

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I will break out the formula into two parts to make the workings very clear to follow. So applying this formula, we can work out the present value of the growing annuity  as follows.  

A/(r-g)  = 87,460/(0.138-0.063) =1,166,133.33

(1- (1+g/1+r)^n)  = 1- (1.063/1.138)^73 =0.9931

PV = A/(r-g) × (1- (1+g/1+r)^n)

166,133.33× 0.9931 =  1,158,092.68  

The present Value of the growing annuity= $1,158,092.68  

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