Question

What is the market value of Investment XYZ if it pays $3,909 per month, starting next month,

for 16 months and the interest rate is 3.87% APR compounded monthly?

Answer 1

$3909 would be paid per month for 16 months, starting next month

Interest rate = 2.31%(compounded monthly)

No of periods = 16 months

Effective Annual Interest rate (EAR) = (1 + Nominal interest rate / 12)¹² -1

Effective Annual Interest rate (EAR) = (1 + 3.87%/12)¹² -1

Effective Annual Interest rate (EAR) = 3.94%

Market value of these investments = Cashflow 1 / (1 + EAR / 12)¹ + Cashflow 2 / (1 + EAR / 12)² + .... + Cashflow 16 / (1 + EAR / 12)¹⁶

Market value of these investments = $3,909 / (1 + 3.94% / 12)¹ + $3,909 / (1 + 3.94% / 12)²   +... + $3,909 / (1 + 3.94% / 12)¹⁶

Using the PVIFA formula =  Annuity * ((1 - (1 + Interest rate)^{-no of periods})) / interest rate)

Market value of these investments = Payment per month * ((1 - (1 + EAR /12)^{-no of periods})) / EAR /12)

Market value of these investments = $3909 * ((1 - (1 + 3.94%/12)^-16)) / 3.94% /12)

Market value of these investments = $60,832.36