Question

1.         I’ve invested $20,000 in a ten-year certificate paying 8% interest, compounding annually until the end of the tern year period. What is the value of the certificate at maturity?

2.         How much money would I have to put in a ten-year certificate paying 8% (compounding annually), in order to redeem that certificate for $10,000 ten years from now?

3.         If I put $10,000 in an 8% certificate (compounding annually), how long until the value of the certificate reaches $20,000?

Answer 1

1.We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

A=20,000*(1.08)^10

=20,000*2.158925

=$43178.5(Approx)

2.Present value=10,000*Present value of discounting factor(rate%,time period)

=10,000/1.08^10

=10,000*0.463193488

=$4631.93(Approx).

3.We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

20,000=10,000*(1.08)^n

(20,000/10,000)=(1.08)^n

Taking log on both sides;

log 2=n*log (1.08)

n=log 2/log (1.08)

=9.01 years(Approx).