From age 20 to 35, Susan deposits $350 semi-annually in a savings account paying 6.12% compounded semi-annually. She then quits making deposits, and leaves the money to continue earning interest until she reaches age 65. William starts later, at age 50, and deposits $2200 semi-annually in an account paying the same rate until he reaches 65. (a) How much money will Susan have accumulated at age 65? $ (b) How much money will William have accumulated at age 65?
From age 20 to 35, Susan deposits $350 semi-annually in a savings account paying 6.12% compounded semi-annually. She then quits making deposits, and leaves the money to continue earning interest until she reaches age 65. William starts later, at age 50, and deposits $2200 semi-annually in an account paying the same rate until he reaches 65.
(a) How much money will Susan have accumulated at age 65?
$
(b) How much money will William have accumulated at age 65?
$
Time value of money concept is used to determine the worth of money today is different from that in future. Money depreciates its value over the period of time due to various reasons such as risk & uncertainty, inflationary measures, more investment opportunities,etc. Hence, value of money today is more than the value of money in future.
Part a)
Susan started investing $350 at the age of 20 for 15 years till the age of 35 at 6.12% compounded semi-annually.
For calculating the future value of money after 15 years the following formula is used:
where,
FV=future value
Annuity=equal monthly investment
r=rate of interest
n=number of years
In the given case,
Annuity=$350
r=6.12%(semi-annually)
n=15*2
=30 years
So, by putting all the given figures in the formula we get,
At the age of 35, Susan has $29,980 and this amount is invested for next 30 years at the same rate compounded semi-annually. For that the following formula is used,
where,
PV=present value of amount invested
n=30*2
n=60 years
By putting these figures in the formula now,
So, Susan will have accumulated $,1,058,440 at the age of 65.
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