Question

Find the payment that should be used for the annuity due whose future value is given. Assume that the compounding period is the same as the payment period. $120,000; monthly payments for 7 years; interest rate 7%. g

Answer 1

$1,104.68

Step-by-step explanation:

The payment applicable to the future value of the annuity due can be determined using the future value formula for the annuity due provided below by rearranging the formula such payment is made the subject:

FV=monthly payment*(1+r)^n-1/r*(1+r)

FV=future value=$120,000

monthly payment=unknown(let us assume it is MP)

r=monthly interest rate=7%/12=0.005833333

n=number of monthly payments in 7 years=7*12=84

$120,000=MP*(1+0.005833333)^84-1/0.005833333*(1+0.005833333)

$120,000=MP*(1.005833333)^84-1/0.005833333*(1.005833333)

$120,000=MP*(1.629994009 -1)/0.005833333*1.005833333

$120,000=MP*0.629994009 /0.005833333*1.005833333

$120,000=MP*108.628973152

MP=$120,000/108.628973152

MP=$1,104.68