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
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