Question

30) Since your first birthday, your grandparents have been depositing $1200 into a savings account on every one of your birthdays. The account pays 6% interest annually. Immediately after your grandparents make the deposit on your 18th birthday, the amount of money in your savings account will be closest to ________.

A) $44,504.14 B) $37,086.78 C) $51,921.49 D) $22,252.07 5

Explanation: N = 18 PMT = $ 1200 I = 6 PV = 0 Compute FV = $37,086.78.

31) Since your first birthday, your grandparents have been depositing $100 into a savings account every month. The account pays 9% interest annually. Immediately after your grandparents make the deposit on your 18th birthday, the amount of money in your savings account will be closest to ________.

A) $32,181 B) $64,362 C) $75,089 D) $53,635

Explanation: N = 216 PMT = $ 100 I = 9/12 PV = 0 Compute FV = $53,635.167

Can someone explain to me why for excercise number 30 we use N=18 and in excercise 31 N=216 (18 years x 12 months)?

I don't see the difference why for one excercise for N we don't need to multiply for 12months and the other one yes. They are worded similarly, but what is the difference between the two N calculations?

Answer 1

In Problem 30. the deposit is made every year.

However, in Problem 31, the the deposit is made every month.

Therefore, Problem 30 is annuity that pays a fixed amount ($1,200) each year, for 18 years, into the account. The amount deposited each year is compounded annually. Therefore, we use N = 18.

However, Problem 31 is annuity that pays a fixed amount ($100) each month, for 18 years, into the account. The amount deposited each month is compounded monthly. As there are 12 months per year, we use N = 18*12 = 216. At the same time, we divide the interest rate (I) by 12 to convert the annual rate into a monthly rate.