Question

Morgan Stanley's wealth management unit offers to invest profits of $750,000 made by an artist on a world tour at 7% compounded semi-annually, locking the money for three years.

1. What will the cash out be?

2. The total interest paid on an investment is the difference between cash out, or A, and cash in, or P; that is, I = A - P. What is the total interest earned by the investment?

(Please work out thoroughly, need to understand the work process)

Answer 1

Answer a) Given,

Investment amt. (P) = $750000

Interest Rate = 7% p.a.

Compounding is done Semi annualy

Time Period = 3years

Now, we have to calculate that how much will be cash out i.e. how much will we receive after 3years on investment of $750000 .

So we know that if the compounding is done the maturity amount will be calculated as

Maturity Amount = P { 1 +( r / 100) } ⁿ

Here the compounding is done semi annualy so the maturity amount will be calculated as

Maturity Amount = P { 1 +( r / 200) } ²ⁿ

So by putting the values above

Maturity amount = $750000 { 1 + (7 / 200) }^2*3

= $921941 ( Figureg are not rounded off )

So Cash out amount will be $ 921941

Answer b) Total Interest earned = Total cash out - Total Cash in

Where ,

Total cash out means the maturity amount of the investment (denoted by A) i.e $921941 (Calculated in answer(a) )

Total Cash in means the Investment amount (denoted by P) i.e. $750000 (Given in Question )

So

Total Interest earned = A - P

= $921941 - $750000

= $171941