Question

Need help!! I can't figure this out

Answer 1

9514 1404 393

Answer:

  12. $1,035,057.23

  13. $988,881.23

  14. $7,762.93

  15. $8,686.16

  16. $967,647.66

Step-by-step explanation:

The annuity and amortization formulas are used for problems like this.

  sum of monthly payments = P((1 +r/12)^(12t) -1)/(r/12)

  monthly amount available = P(r/12)/(1 -(1 +r/12)^(-12t))

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12. The sum of monthly payments of 74, accumulated at 9% compounded monthly for 52 years is ...

  A = ($74)((1 +.09/12)^(12·52) -1)/(.09/12) = $1,035,057.23

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13. The total of payments is ...

  $74×12×52 = $46,176

So, the interest earned is ...

  $1,035,057.23 -46,176 = $988,881.23

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14. The amount available in perpetuity is the monthly interest on this account balance.

  $1,035,057.23 × .09/12 = $7,762.93

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15. The monthly amount available for 25 years is found from the amortization formula:

  A = $1,035,057.23(.09/12)/(1 -(1 +.09/12)^(-12·25)) = $8686.16

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16. The amortization formula is used for this, too.

  8066 = P(.094/12)/(1 -(1 +.094/12)^(-12·30)) = 0.00833568P

  P = $8066/0.00833568 = $967,647.66