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A loan of $12,000 with interest at 14% compounded annually is to be amortized by equal payments at the end of each year for six years. What will the balance outstanding be after second year?

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To calculate the balance outstanding after the second year of equal payments, we can use the formula for the future value of an annuity:

FV = PMT x [(1 + r)^n - 1] / r

Where:
FV = future value of the annuity
PMT = the equal payment amount
r = the interest rate per period (in this case, the annual interest rate divided by the number of payment periods per year)
n = the total number of payment periods

In this case, we have:
PMT = the equal payment amount
r = 14% / 1 = 14% per year (since interest is compounded annually)
n = 6 years
We need to first calculate the PMT using the formula for the present value of an annuity:

PMT = PV x [r / (1 - (1 + r)^(-n))]

Where:
PV = present value of the annuity

To find PV, we can use the formula for the present value of a lump sum:

PV = FV / (1 + r)^n

Where:
FV = the total loan amount
r = 14% per year
n = 6 years

Plugging in the values, we get:

PV = $12,000 / (1 + 0.14)^6
PV = $5,070.33

Now we can calculate PMT using the present value:

PMT = $5,070.33 x [0.14 / (1 - (1 + 0.14)^(-6))]
PMT = $2,360.63

Therefore, the equal payment amount is $2,360.63 per year.

To calculate the balance outstanding after the second year of payments, we can use the formula for the future value of an annuity with two years of payments:

FV = PMT x [(1 + r)^n - 1] / r

Where:
FV = the future value of the annuity after two years of payments
PMT = $2,360.63
r = 14% / 1 = 14% per year (since interest is compounded annually)
n = 2 years

Plugging in the values, we get:

FV = $2,360.63 x [(1 + 0.14)^2 - 1] / 0.14
FV = $4,950.53

Therefore, the balance outstanding after the second year of payments is $4,950.53.
User Bezalel
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