Question

Congratulations, you are a millionaire. No, the Delaware Lottery office did not call. However, an officer from Bank of America has just informed you of an account that your grandmother set up years ago to be given to you on this date. The balance is exactly one million dollars. She made ten equal annual deposits into the account, with the final one occurring exactly 50 years ago in 1970. The account has earned 3.2% (APY) every year.A. How much money was in the account on this date in 1970?
B. How much was each of the ten annual payments that Grandma made (1961-1970)?

Answer 1

Part A

Answer:

$207,021

Explanation:

The balance on the account at the end of the year 2020 is $1,000,000

The question asks us to calculate the balance on the account at the end of the year 1970, which is exactly 50 years ago.

We would simply discount the $1,000,000 by using an interest rate of 3.2%

$PV_{1970}$ = $\frac{1000000}{(1 + 0.032)^{50} }$ = $207,021

Part B

Answer:

$17,892.88

Explanation:

We have the value at year 1970 which is $207,021

Now to calculate the annual payment (PMT) we would plug the following values in the financial calculator,

PV = 0

N = 10

FV =207021

I/Y = 3.2

PMT = ?

PMT = $17,892.88

https://www.calculator.net/finance-calculator.html?ctype=contributeamount&ctargetamountv=207021&cyearsv=10&cstartingprinciplev=0&cinterestratev=3.2&ccontributeamountv=1000&ciadditionat1=end&printit=0&x=102&y=11