Question

7.) Your grandmother has been putting $ 1 comma 000 into a savings account on every birthday since your first​ (that is, when you turned​ one). The account pays an interest rate of 3 %. How much money will be in the account immediately after your grandmother makes the deposit on your 18th birthday
The amount in the account upon your 18th birthday is ​$____(Round to the nearest​ dollar.)

8.) A rich relative has bequeathed you a growing perpetuity. The first payment will occur in a year and will be $ 4 comma 000. Each year after​ that, you will receive a payment on the anniversary of the last payment that is nbsp 5 % larger than the last payment. This pattern of payments will go on forever. Assume that the interest rate is nbsp 9 % per year.
a. What is​ today's value of the​ bequest?
b. What is the value of the bequest immediately after the first payment is​ made?
a. What is​ today's value of the​ bequest?
​Today's value of the bequest is ​$____ ​(Round to the nearest​ dollar.)

Answer 1

Answer to Question 7:

Annual Saving = $1,000
Interest Rate = 3%
Period = 18 years

Future Value = $1,000*1.03^17 + $1,000*1.03^16 + … + $1,000*1.03 + $1,000
Future Value = $1,000 * (1.03^18 - 1) / 0.03
Future Value = $1,000 * 23.414
Future Value = $23,414

The amount in the account upon your 18th birthday is $23,414

Answer to Question 8:

Part a.

Expected Payment in 1 year = $4,000
Growth Rate = 5%
Interest Rate = 9%

Value of Bequest Today = Expected Payment in 1 year / (Interest Rate - Growth Rate)
Value of Bequest Today = $4,000 / (0.09 - 0.05)
Value of Bequest Today = $100,000

Part b.

Expected Payment in 1 year = $4,000
Growth Rate = 5%
Interest Rate = 9%

Expected Payment in 2 years = Expected Payment in 1 year * (1 + Growth Rate)
Expected Payment in 2 years = $4,000 * 1.05
Expected Payment in 2 years = $4,200

Value of Bequest in 1 year = Expected Payment in 2 years / (Interest Rate - Growth Rate)
Value of Bequest in 1 year = $4,200 / (0.09 - 0.05)
Value of Bequest in 1 year = $105,000