Question

Future value.   Jack and Jill are saving for a rainy day and decide to put ​$45 away in their local bank every year for the next 25 years. The local​ Up-the-Hill Bank will pay them 5 ​% on their account. a.  If Jack and Jill put the money in the account faithfully at the end of every​ year, how much will they have in it at the end of 25 ​years? b. ​ Unfortunately, Jack had an accident in which he sustained head injuries after only 10 years of savings. The medical bill has come to ​$500 . Is there enough in the​ rainy-day fund to cover​ it? a. If Jack and Jill put the money in the account faithfully at the end of every​ year, how much will they have in it at the end of 25 ​years? ​$nothing ​(Round to the nearest​ cent.)

Answer 1

Part A:

FV of Annuity :
Annuity is series of cash flows that are deposited at regular intervals for specific period of time.

FV of Annuity = CF [ (1+r)^n - 1 ] / r
r - Int rate per period
n - No. of periods

Amount in Account after 25 years:

Particulars	Amount
Cash Flow	$           45.00
Int Rate	5.000%
Periods	25

FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r
= $ 45 * [ [ ( 1 + 0.05 ) ^ 25 ] - 1 ] / 0.05
= $ 45 * [ [ ( 1.05 ) ^ 25 ] - 1 ] / 0.05
= $ 45 * [ [3.3864] - 1 ] / 0.05
= $ 45 * [2.3864] /0.05
= $ 2147.72

Part B:

Amount in Account after 10 years:

Particulars	Amount
Cash Flow	$           45.00
Int Rate	5.000%
Periods	10

FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r
= $ 45 * [ [ ( 1 + 0.05 ) ^ 10 ] - 1 ] / 0.05
= $ 45 * [ [ ( 1.05 ) ^ 10 ] - 1 ] / 0.05
= $ 45 * [ [1.6289] - 1 ] / 0.05
= $ 45 * [0.6289] /0.05
= $ 566.01

As amount in account > $ 500, It will be able to meet medical exp of $ 500.