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student borrows $65,000 for business school at 8.5% stated annual interest with monthly repayment over 8 years. Consider this as a loan with no payments or interest during school so that the problem structure is equivalent to a standard loan received one period before the first payment. Suppose that to better match expected student salary growth over time, the loan is structured as a growing annuity with each monthly payment growing by 0.2% compared to the previous monthly payment. How much is the first monthly payment?

Sagot :

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Answer:

[tex]First\ monthly\ payment= $858.69[/tex]

Step-by-step explanation:

From the Question we are told that

Borrows $65,000

Annual interest  8.5%

Monthly repayment over 8 years

Generally PV of annuity with growth is mathematically represented as

where PV is present value

PV of annuity with growth X= [tex](P/ (r-g)) * (1- ((1+g)/(1+r))^n)[/tex]

     [tex]\frac{P}{\frac{8\%}{y12-0.2\%} } *(1-((1+0.2\%)/(1+8.5\%/12))^(^8^*^1^2^)^)=65000[/tex]

    [tex]196.7213115P* 0.384791918=65000[/tex]

     [tex]196.7213115P=65000/0.384791918[/tex]

    [tex]196.7213115P=168922.4668[/tex]

     [tex]P= 168922.4668/196.7213115[/tex]

    [tex]P= 858.6892063[/tex]

[tex]First\ monthly\ payment= $858.69[/tex]

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