Marry pays 5000 at the end of every month to a bank as loan repayment the interest rate of 10% compounded monthly and t=4 months. Find the present value?
To find the present value, we need to calculate the amount that Marry needs to borrow from the bank.
The formula to calculate the present value of an annuity is:
PV = PMT * (1 - (1 + r)^(-n)) / r
Where:
PV = Present Value
PMT = Payment amount per period
r = Interest rate
n = Number of periods
In this case, Marry pays $5000 at the end of every month, the interest rate is 10% compounded monthly, and the loan duration is 4 months.
PMT = $5000
r = 10% (convert to decimal form: 0.10)
n = 4
Using the formula:
PV = $5000 * (1 - (1 + 0.10)^(-4)) / 0.10
PV = $5000 * (1 - (1.10)^(-4)) / 0.10
PV = $5000 * (1 - 0.68301) / 0.10
PV = $5000 * 0.31699 / 0.10
PV = $1584.95
Therefore, the present value of Marry's loan is approximately $1,584.95.