Jo has borrowed k2500 and is being charged interest at 7.8% interest, compounded weekly
a. How much will she owe after 6 months
b. If she pays k1000 after 6 months, how much will she owe after another 6 months?
a. To calculate how much Jo will owe after 6 months, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount owed after n years
P = the principal amount (k2500)
r = the annual interest rate (7.8% or 0.078)
n = the number of times the interest is compounded per year (52 weeks in a year)
t = the number of years (6 months = 0.5 years)
Plugging in the values, we get:
A = 2500(1 + 0.078/52)^(52*0.5)
A ≈ 2500(1 + 0.0015)^26
A ≈ 2500(1.0015)^26
A ≈ 2500(1.043579)
A ≈ 2608.95
After 6 months, Jo will owe approximately k2608.95.
b. If Jo pays k1000 after 6 months, the remaining balance will be:
Remaining balance = 2608.95 - 1000
Remaining balance = 1608.95
To calculate how much she will owe after another 6 months on the remaining balance, we use the same formula:
A = 1608.95(1 + 0.078/52)^(52*0.5)
A ≈ 1608.95(1 + 0.0015)^26
A ≈ 1608.95(1.0015)^26
A ≈ 1608.95(1.043579)
A ≈ 1676.71
After another 6 months, Jo will owe approximately k1676.71 on the remaining balance of k1608.95.