An insurance company has offered your friend the choice of $45,000 per year for 15 years, with the first payment being made toda
y, or a lump sum. If a fair return is 7.5%, how large must the lump sum be to leave him as well off financially as with the annuity?
1 answer:
Answer:
$427,011.92
Explanation:
We use the present value formula i.e to be shown in the attached spreadsheet
Given that,
Future value = $0
Rate of interest = 7.5%
NPER = 15 years
PMT = $45,000
The formula is shown below:
= -PV(Rate;NPER;PMT;FV;type)
And, in type we write the 1 instead of 0
So, after solving this, the present value is $427,011.92
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Answer:
A) One year ago, Saul's investment was worth less than Trek's investment. B)
Explanation:
Computation of Saul's Investment Rate of Interest
A = P(1 + r)^t
Where: A = Final amount
P = Principal amount
r = Interest rate
t = Time period in years.
A = $800
P = $500
r = Unknown
t = 4 years
800 = 500(1 + r)^4
Divide both sides by 500
800/500 = (500(1 + r)^4 )/500
1.6 = (1 + r)^4
Take the fourth root of both sides
=
1.1246826504 = (1 + r)
1.1246826504 = 1 + r
Subtract 1 from both sides
1.1246826504 - 1 = 1 -1+ r
0.1246826504 = r
Convert 0.1246826504 to percentage and to 2 decimal places
r = 12.47%
That is, Saul investment is at 12.47% interest rate
Computation of Trek's Investment Rate of Interest
A = $800
P = $600
r = Unknown
t = 4 years
800 = 600(1 + r)^4
Divide both sides by 600
800/600 = (600(1 + r)^4 )/600
1.333333333 = (1 + r)^4
Take the cube root of both sides
=
1.100642416 = (1 + r)
1.100642416 = 1 + r
Subtract 1 from both sides
1.100642416 - 1 = 1 -1+ r
0.100642416 = r
Convert 0.100642416 to percentage and to 2 decimal place
r = 10..06%
That is, Trek investment is at 10..06% interest rate
It can be observed that Saul earns a higher rate of return than Trek. The fact that both investment have equal returns today, it means Saul's investment was worth less than Trek's investment one year ago.