Question

XERCISE 1:

You want to accumulate a 200.000 euros retirement fund and you plan to make the first deposit on March 1, 1984 and the last on September 1, 2005. Find the size of each deposit, if he makes the deposits

(a) semi-annually in a fund that pays 12.5% per annum compounded semi-annually

(b) monthly in a fund that pays 12.5 % per annum compounded monthly.

EXERCISE 2:

Your friend makes regular deposits of 500$ at the end of each half-year for 5 years and then $800 for the next 3 years. Find the accumulated value of her deposit if interest is at 11%

Answer 1

(a) Semi-annually in a fund that pays 12.5% per annum compounded semi-annually

FV = PMT * [(1+i) ^n – 1] /i

Where FV = future value of semiannual payments =200 euros

PMT or semiannual payments =?

And i= I/Y = 12.5% is the interest rate per annum, as it is compounded semiannually therefore semiannual interest rate = 12.5%/2 = 6.25%

The time period (number of payments) n = 2*22 years = 44

Therefore,

200= PMT * [(1+.0625) ^44 -1]/ 0.0625

PMT = 13.43

Therefore semiannual payments are 13.43

(b) Monthly in a fund that pays 12.5 % per annum compounded monthly.

And i= I/Y = 12.5% is the interest rate per annum, as it is compounded monthly therefore monthly interest rate = 12.5%/12 = 1.04%

The time period (number of payments) n = 12*22 years = 264

Therefore,

200= PMT * [(1+.0104) ^264 -1]/ 0.0104

PMT = 2.23

Therefore monthly payments are 2.23

EXERCISE 2:

Your friend makes regular deposits of 500$ at the end of each half-year for 5 years and then $800 for the next 3 years. Find the accumulated value of her deposit if interest is at 11%

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

Where,

Present value (PV) =?

Payment PMT = $500, $800

n = 10 & 6

Annual interest rate I =11%, therefore half yearly interest rate i=11%/2 = 5.50%

Therefore

PV = $500 * [1- (1+5.5%) ^-10]/5.5% + $800 * [1- (1+5.5%) ^-6]/5.5%

PV = $3,768.81+ $3,996.42

= $7,765.24