Kelven puts $7500 into an investment, paying 4.7% per annum, compounding monthly.He makes regular additional contributions to the investment each month. After oneyear, Kelven’s investment is worth $13 991.15 to the nearest cent.a Find the amount of Kelven’s regular monthly payment. Round your answer correctto the nearest cent.b i Find the amount that Kelven invested in the first year through monthlypayments.ii Find the increase in the value of the investment in the first year.iii Hence, find how much interest was earned in the first year. Round your answercorrect to the nearest cent.c Given Kelven’s monthly payment found in a, how many months will it take forKelven’s investment to be worth at least $20 000?
Question
Kelven puts 13 991.15 to the nearest cent.a Find the amount of Kelven’s regular monthly payment. Round your answer correctto the nearest cent.b i Find the amount that Kelven invested in the first year through monthlypayments.ii Find the increase in the value of the investment in the first year.iii Hence, find how much interest was earned in the first year. Round your answercorrect to the nearest cent.c Given Kelven’s monthly payment found in a, how many months will it take forKelven’s investment to be worth at least $20 000?
Solution
a) To find the amount of Kelven's regular monthly payment, we first need to calculate the value of the initial investment after one year. The formula for compound interest is
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