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Based on the value of the annuity, the amount it earns, and the compounding period, the money paid to Nathan each month will be B. $5,840.62.
The amount Nathan will be paid is an annuity because it is constant.
First find the monthly interest and the compounding period in months:
= 4.8/12 months
= 0.4%
Number of compounding periods:
= 20 x 12
= 240 months
The monthly payment is:
Present value of annuity = Annuity x ( 1 - (1 + rate) ^ -number of periods) / rate
900,000 = A x ( 1 - (1 + 0.4%)⁻²⁴⁰) / 0.375%
900,000 = A x 154.0932
A = 900,000 / 154.0932
= $5,840.62.
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If APR is compounded monthly for a period of 20 years. The amount of money that Nathan will be paid each month is: B. $5,840. 62.
Using the formula
PMT=PV÷[(1-(1+r/k)^(-kn))÷(r/k)]
Where:
Present value (pv)=$900,000
Interest rate (r)=4.8% or 0.048
Number of month (k)=12 months
Number of years (n)= 20 years
Let plug in the formula
PMT=900,000÷[(1−(1+0.048÷12)^(-12×20))÷(0.048÷12)]
PMT=900,000÷[(1−(1.004)^(-240))÷(0.004)]
PMT=900,000÷154.093
PMT=$5,840.62
Therefore the amount of money that Nathan will be paid each month is: B. $5,840. 62.
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