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. $19,000; quarterly payments for 9 years; interest rate 5.8% The payment should be $___ (Round to the nearest cent as needed.)

Answer 1

SOLUTION:

From given data,

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. $19,000; quarterly payments for 9 years; interest rate 5.8% .

Where,

Interest rate = k = 5.8% = 5.8/100 = 0.058

n = 9*4 = 36

FV = $ 19000

We know the formula for payment:

payment = FV / (((1+k)ⁿ-1 / k)(1+k))

payment = 19000/ (((1+0.058)³⁶-1 / 0.058)(1+0.058))

payment = 19000/ 120.6072866

payment = $ 157.536

payment $ 158