Question

5. We wish to accumulate a fund of $60,000 by making regular deposits of $1,525 at the end of each month for as long as is necessary. If the annual rate of interest is 6% compounded monthly, how many regular deposits will be necessary and find the final deposit to be made one month after the last regular deposit.

Answer 1

1) When compounded monthly, Effective monthly interest rate = [(1 + Annual interest rate/12)2-1] / 12 Monthly interest rate, RATE 0.51398% [((1+6%/12)^12) - 1] /12 ==> [((1+0.5%)^12) - 1] / 12 ==> [(1.005^12) - 1] / 12 = 0.0051398 = 0.51398%] Monthly installment amount, PMT $1,525 Initial balance in account, PV $0 Maturity value at the end, FV $60,000 Monthly installment type, TYPE 0 = 0 if paid at the end of each month; 1 if paid at the beginning of each month. Number of monthly deposits required 35.92 (Ref: NOTE] NOTE: Number of monthly deposits required is calculated using EXCEL FUNCTION NPER(rate,pmt,pv,fv,type) where rate = 0.51398%; pmt = 1525; pv = 0; fv = -60000; type=0; Here, pmt is positive as it denotes cash outflow; fv is negative as it denotes cash inflow; type=0 as installments are paid at the end of each month only. A 1 Monthly interest rate, RATE 2 Monthly installment amount, PMT 3 Initial balance in loan account, PV 4 Balance in account at the end, FV 5 Monthly installment type, TYPE 6 Number of monthly deposits required 7 в C D E F G H I J K =(((1+6%/12)^12)-1)/12 [((1+6%/12)^12) - 1] /12 ==> [((1+0.5%)^12) - 1] / 12 ==> [(1.005^12) - 1] / 12 = 0.0051398 = 0.51398%] $1,525 $0 $60,000 0 = 0 if paid at the end of each month; 1 if paid at the beginning of each month. =NPER(B1,B2,B3,-B4,B5) [Ref: NOTE] 2) Amount of final deposit required after the regular monthly installment = Fraction of last installment x Monthly installment amount. Fraction of last installment 0.92 [Fraction left after making 35th normal payment] Monthly installment amount $1,525 Amount of final deposit required after the regular monthly installment $1,410 (0.92 x $1525]