Question

6. A periodic deposit is made into an annuity with the given terms. Find how much should be regularly deposited in order to have the specified final amount in the account. Round your answer to the nearest dollar.Future value:$122,000Interest rate:2.45%FrequencymonthlyTime:17 yearsRegular deposit amount: $

Answer 1

Remember that

The formula for the future value of an ordinary annuity is equal to:

`FV=P\lbrack((1+ (r)/(n) )^(nt) -1)/( (r)/(n) )\rbrack`

where

FV is the future value

P s the periodic payment

r is the interest rate in decimal form

n is the number of times the interest is compounded per year

t is the number of years

In this problem we have

FV=$122,000

r=2.45%=0.0245

n=12

t=17 years

P=?

substitute the given values

`122,000=P\lbrack((1+(0.0245)/(12))^((12\cdot17))-1)/((0.0245)/(12))\rbrack`

solve for P

P=$482.72 ------> round to the nearest dollar

P=$483