The main TVM problems relating to healthcare are: a) present value of a lump sum

Question

The main TVM problems relating to healthcare are: a) present value of a lump sum b) present value of an annuity stream c) future value of a lump sum d) future value of an annuity stream. Provide an example of each of these TVM problems.

The Smith family is interested in buying a home. The family is applying for a $200,000 30-year mortgage. Under the terms of the mortgage, they will receive $200,000 today to help purchase their home. The loan will be fully amortized over the next 30 years. Current mortgage rates are 7.5%. Interest is compounded monthly and all payments are due at the end of the month. What is the monthly mortgage payment?

Miriam has saved $5,000 and intends to use his savings as a down payment on a new car. After careful examination of his income and expenses, She has concluded that the most he can afford to spend every month on his car payment is $425. The car loan that she uses to buy the car will have an APR of 10%. What is the price of the most expensive car that Henry can afford if he finances his new car for 48 months?

Explanation / Answer

Monthly payment = (rate + rate/((1+rate)^months-1))* principal

here in the question 7.5% annual rate to convert it ino monthly rate divide by 12.

=.00625

Total months would be 12*30 = 360

      .00625

.00625 + ((1.00625 ^360)-1) × $200,000

4) The middle section of the equation is the most difficult to solve so we will calculate that first.

(.00625) ÷ ((1.00625 ^360)-1) =

(.00625) ÷ (9.421533905 -1) =

(.00625) ÷ 8.421533905 =

0.000742145

5) "Plugging" this into the rest of the equation we have:

(.00625 + 0.000742145) × $200,000 =

(0.006992145) × $200,000 =

$ 1,398.43 Montly repayment

Part 2)

Same formula would be used again to find the princpal

Monthly payment = (rate + rate/((1+rate)^months-1))* principal

425 is the monthly repayment

rate is 10%, monthly rate would be 10%/12 = 0.0083333

425 = .0083333

.0083333 + ((1.0083333 ^48)-1) × Principal

4) The middle section of the equation is the most difficult to solve so we will calculate that first.

(.0083333) ÷ ((1.0083333 ^48)-1) =

(.0083333) ÷ (1.489354099 -1) =

(.0083333) ÷ 0.489354099 =

0.01702925

5) "Plugging" this into the rest of the equation we have:

(.008333 + 0.01702925) × principal =

(0.025362583) × prinicpal = 425

Principal = 425/0.025362583

= 16,757

So the price of the expensive car henry can afford is 5,000 + 16757 = $ 21,757

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