Answered

IDNLearn.com: Your trusted source for finding accurate answers. Our platform provides trustworthy answers to help you make informed decisions quickly and easily.

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 :

Okpalawalter8idn

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]

We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Find reliable answers at IDNLearn.com. Thanks for stopping by, and come back for more trustworthy solutions.