Question

You plan to buy a house in 11 years. You want to save money for a down payment on the new house. You are able to place $286 every month at the end of the month into a savings account at an annual rate of 6.54 percent, compounded monthly. How much money will be in the account after you made the last payment?

Answer 1

Number of payment = 11* 12 = 132

Monthly interest rate = 6.54/ 12 = 0.545% per month

Annuity is series of equal cash flows for certain period of time, if periodic cash flow is P, number of period is n, and interest per period is r then future value of cash flow will be

FV of annuity = P [(1 + r)^n - 1]/ r

Let's put the values in the formula,

= 286[(1 + 0.00545)^132 - 1]/ 0.00545

= 286[(1.00545 )^132 - 1]/ 0.00545

= 286 (2.04919437616085) - 1/ 0.00545

= 286 ( 1.04919437616085 )/ 0.00545

= 286 * 192.512729570798

= 55058.64

You will have 55058.64 in your account.