t Ullered an investment that will pay you $200 the first year, $400 the next yea

Question

t Ullered an investment that will pay you $200 the first year, $400 the next year and $5000 the third year (all payments will be end-of-year). You can earn 6% on for this one? a) United Bank offers you a $500,000, thirty year amortized loan at 7% annual interest. What will your MONTHLY loan payment be? ) In order to accumulate $2,000,000 for retirement in 45 years, a young investor c) A life insurance company is trying to sell you an investment policy that will pay yo save every year into a savings program yielding wishes to know how much to 4% per year 0 000 per year, in perpetuity, If your required return on this investme is 596, how much will you pay for the policy?

Explanation / Answer

5.

a)

Loan Amount = 500000

Interest = 7%. Monthly interest = 7%/12 = 0.5833%

Period = 30 years = 30*12 = 360 months

Monthly payment can be calculated using the PV of Annuity formula:

PV = C * ((1-1/(1+r)T)/r) where C = Monthly payment, r = periodic interest rate, T = number of periods

Here. PV = 500000, r = 0.5833% & T = 360

So, C = 500000/((1-1/(1+0.5833%)360)/0.5833%) = $3326.51  [rounded off to 2 decimals]

b)

We can calculate the annual payment by using FV of annuity formula:

FV = C * (((1+r)T - 1)/r) where C = Annuity Payment, r = periodic Interest Rate & T = number of periods

FV = 2000000, r = 4%, T = 45

So, C = 2000000/(((1+4%)45 - 1)/4%) = $16524.91   [rounded off to 2 decimals]

c)

We can calculate the payment by using formula for present value of perpetuity:

PV = C/r

Here, C = 10000 & r = 5%

So, Payment = 10000/5% = $200000

* I am not sure that you want the answer of the last part of 4th question as it was partially cut in the picture. Assuming that you want the answer:

Discount Rate = 6%

The most you shpuld pay for this investment should be equal to the PV of the payments discounted by 6%.

PV of payments = 200/(1+6%)1 + 400/(1+6%)2 + 5000/(1+6%)3 = $4742.77 [rounded to 2 decimals]

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