A = P (1 + r/n) (nt) ? 1. Let m=nt. Let R be the payment per period. If the prin

Question

A = P (1 + r/n) (nt)

?1. Let m=nt. Let R be the payment per period. If the principle P is the total amount of money invested, briefly explain why R=P/m. Hint: P is the total amount and m is number of compoundings.

NAME: 1.3. Imagine you make a payment with k compoundings left. What is the future value of this one individual payment? Hint: Use the compound interest formula. Think of P in that formula as R. How many compounds are left? 1.4. Let i = r/n. Briefly explain why, because of your last answer, the future value A of an ordinary annuity is: A = R + R(1 i) + R(1+92 + + R(1+i)m-1

Explanation / Answer

As one is investing P in a year

and if he divides that investment in m periods in a year

he will invest P/m per period

Hence, R=P/m

Future value=R*(1+r/n)^k

Future value of payment iif 1 compounding is left=R*(1+r/n)

Future value of payment iif 2 compounding is left=R*(1+r/n)^2

Future value of payment iif 3 compounding is left=R*(1+r/n)^3

hence, total future valiue=R*(1+r/n)+R*(1+r/n)^2+R*(1+r/n)^3....=R+R*(1+i)+R*(1+i)^2....

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