Question

Perry wants to make a settlement on an insurance claim. He was offered one of two choices. He could either accept a lump-sum amount of $10000 now, or accept quarterly payments of $290 for the next 10 years. If the money is placed into a trust fund earning 3.95% compounded semi-annually, which is the better option and by how much?

Answer 1

As the interest rate is semi-annually compounded, therefore first we will calculate Effective annual rate (EAR)

Effective annual rate (EAR) = (1 + r/m) ^m – 1

Where,

Effective annual rate (EAR) =?

Where, annual percentage rate (APR); r= 3.95%

For semiannual compounding; number of compounding per year, m = 2

Therefore

EAR= (1 + 3.95%/2) ^2 - 1

= 0.0399 or 3.99%

Now calculate the present value (PV) of quarterly payments of $290 for the next 10 years in following manner

PV = PMT * [1-(1+i) ^-n)]/i

Where,

Present value (PV) =?

PMT = Quarterly payment =$290

n = N = number of payments = 4 *10 years = 40 payments

Effective Annual interest rate = 3.99%; therefore quarterly interest rate = 3.99%/4 = 0.997 per quarter

Therefore,

PV = $290 * [1- (1+0.997%) ^-40]/0.997%

= $9,527.03

Present quarterly payments of $290 for the next 10 years is $9,527.03

And the payment of lump-sum amount now is $10000

We can see that the lump-sum amount is more worthy than the quarterly payments as the present value of lump-sum amount is more therefore option 1 with lump-sum amount is better option.

Option 1 is better by $10000 - $9,527.03 = $472.97