r = 0.1349/ 12 months per year = 0.01124
n = 4 yrs * 12 months = 48
Use PV ordinary annuity: PVoa = PMT[(1 - (1 / (1 + r)^n)) / r]
15,582 = PMT[(1 - (1 / 1.01124^48)) / 0.01124
15582 = PMT[( 1- (1 / 1.71016)) / 0.01124]
15582 = PMT[(1 - 0.58474) / 0.01124]
15582 = PMT[0.41526 / 0.01124]
15582 = PMT[36.93944]
15582 / 36.93944 = PMT
PMT = $421.82551, round to $421.83
2) r = 0.0588 /12 = 0.0049
n = 5 * 12 = 60
PVoa...
15582 = PMT[(1 - (1 / 1.0049^60)) / 0.0049]
15582 = PMT[(1 - 0.74581) / 0.0049]
15582 = PMT[51.87515]
PMT = 15582 / 51.87515
PMT = $300.37503, round to $300.38
3) effective annual rate "EAR": [(1 + (0.0075/12)^12] - 1
= (1.00063^12) - 1
= 0.00753
time = ln(FV / PV) / ln(1 + r)
t = ln(22,888 / 7306) / ln(1.00753)
t = ln(3.13277) / ln(1.00753)
t = 1.14192 / 0.0075
t = 152.30315 years - you won't get it, but your great grandchildren might! :)
check math: FV = PV(1 + r)^n
FV = 7306(1.00753^152.30315)
FV = 7306(3.13277)
FV= $22,888
1. 15,582 = A * (1 - (1+.1349/12))^(-48) / (.1349/12). Solve for A, which is the amount of the payment.
2. 15,582 = A * (1 - (1+.0588/12)^(-60) / (.0588/12).
3. 22,888 = 7,306 * (1.0075)^N. Solve for N.
I need help solving these three equations.
Equation 1
I need to borrow $15,582 from a bank with a credit card. The interest rate is 13.49% and being compounded monthly over 4 years.
Equation 2
I need to borrow $15,582 from a bank via a personal loan. The interest rate is 5.88% and being compounded monthly over 5 years.
Equation 3
I need to invest $7,306 in a term deposit returning 0.75% compounded monthly.
Thank you.
