Question

You decide to deposit $100 in the bank today and to make 10 additional deposits every 6 months beginning 6 months from now, the first of which will be $75 and increasing $25 per deposit after that. A few minutes after making the last deposit, you decide to withdraw all the money deposited. If the bank pays 6% nominal interest compounded semiannually, how much money will you receive?

Answer 1

Equivalent uniform series payments of the gradient of $25, along with the first payment of $75 in that series is $181.41 as follows:

E17 f =E15+E16 A B C D E 1 Uniform series of payments required for the gradient (increase in amount)= 2 =G* {(1/i )-n/((1+i)^n)-1} 3 Where G= gradient (increase in periodical amount), 4 is interest rate and n=number of periods of payment. 5 Given, 6 Gradient G= $ 25.00 7 Period (number of quarters) Given n= 10 8 Interest rate per quarter 6%/2 i= 3.0% 9 Calculations: Formula Cell reference Values 10 1/E8 33.333333 (1+i)^n (1+E8)^E7 1.3439164 (1+i)^n-1 E11-1 0.3439164 13 n/(1+i)^n-1 E7/E12 29.076836 14 (1/i)-n/(1+i)^n-1 E10-E13 4.2564978 15 Uniform series payments G*((1/1)-(n/(1+i)^n-1)) E6*E14 $ 106.41 16 Initial payments Given $ 75.00 17 Equivalent uniform payment= E15+E16 $ 181.41 1/i 11 12

Taking the initial payment of $100 as PV, amount received immediately after the last payment (that is, on completion of 5 years) is $ 2,214.08 calculated using FV function of Excel as follows:

N D11 f =FV(D7,D6,D8,D9,010)*-1 A B с 1 Amounts in $ Function Formula arguments Value 3 Number of years (N) Given 5 4 Payment frequency Given Semi annual 5 Number of payments a year (n) 2 6 Number of payments Nin NPER 10 7 Interest rate per period 6%/2 Rate 3% 8 Amount of periodical contribution Given PMT $ 181.41 9 Present value (First payment) PV 100 10 Timing of payments (End of period) Given Type 0 11 Accumulated value at the end of term FV $ 2,214.08 4